How to customize Bootstrap 3 tab color

On the selector .nav-tabs > li > a:hover add !important to the background-color.

.nav-tabs{
  background-color:#161616;
}
.tab-content{
    background-color:#303136;
    color:#fff;
    padding:5px
}
.nav-tabs > li > a{
  border: medium none;
}
.nav-tabs > li > a:hover{
  background-color: #303136 !important;
    border: medium none;
    border-radius: 0;
    color:#fff;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
<link href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" rel="stylesheet"/>

<ul class="nav nav-tabs" id="myTab">
    <li class="active"><a data-toggle="tab" href="#search">SEARCH</a></li>
    <li><a data-toggle="tab" href="#advanced">ADVANCED</a></li>
</ul>
<div class="tab-content">
    <div id="search" class="tab-pane fade in active">
        Aliquip placeat salvia cillum iphone. Seitan aliquip quis cardigan american apparel,
        butcher voluptate nisi qui.
    </div>
    <div id="advanced" class="tab-pane fade">
        Vestibulum nec erat eu nulla rhoncus fringilla ut non neque. Vivamus nibh urna.
    </div>
</div>

I think you should edit the anchor tag on bootstrap.css. Otherwise give customized style to the anchor tag with !important (to override the default style on bootstrap.css).

Example code

.nav {
    background-color: #000 !important;
}

.nav>li>a {
    background-color: #666 !important;
    color: #fff;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<link rel="stylesheet" href="//maxcdn.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css">

<script src="//maxcdn.bootstrapcdn.com/bootstrap/3.2.0/js/bootstrap.min.js"></script>


<div role="tabpanel">

  <!-- Nav tabs -->
  <ul class="nav nav-tabs" role="tablist">
    <li role="presentation" class="active"><a href="#home" aria-controls="home" role="tab" data-toggle="tab">Home</a></li>
    <li role="presentation"><a href="#profile" aria-controls="profile" role="tab" data-toggle="tab">Profile</a></li>
    <li role="presentation"><a href="#messages" aria-controls="messages" role="tab" data-toggle="tab">Messages</a></li>
    <li role="presentation"><a href="#settings" aria-controls="settings" role="tab" data-toggle="tab">Settings</a></li>
  </ul>

  <!-- Tab panes -->
  <div class="tab-content">
    <div role="tabpanel" class="tab-pane active" id="home">...</div>
    <div role="tabpanel" class="tab-pane" id="profile">tab1</div>
    <div role="tabpanel" class="tab-pane" id="messages">tab2</div>
    <div role="tabpanel" class="tab-pane" id="settings">tab3</div>
  </div>

</div>

Fiddle: http://jsfiddle.net/zjjpocv6/2/


.panel.with-nav-tabs .panel-heading {
  padding: 5px 5px 0 5px;
}

.panel.with-nav-tabs .nav-tabs {
  border-bottom: none;
}

.panel.with-nav-tabs .nav-justified {
  margin-bottom: -1px;
}


/********************************************************************/


/*** PANEL DEFAULT ***/

.with-nav-tabs.panel-default .nav-tabs>li>a,
.with-nav-tabs.panel-default .nav-tabs>li>a:hover,
.with-nav-tabs.panel-default .nav-tabs>li>a:focus {
  color: #777;
}

.with-nav-tabs.panel-default .nav-tabs>.open>a,
.with-nav-tabs.panel-default .nav-tabs>.open>a:hover,
.with-nav-tabs.panel-default .nav-tabs>.open>a:focus,
.with-nav-tabs.panel-default .nav-tabs>li>a:hover,
.with-nav-tabs.panel-default .nav-tabs>li>a:focus {
  color: #777;
  background-color: #ddd;
  border-color: transparent;
}

.with-nav-tabs.panel-default .nav-tabs>li.active>a,
.with-nav-tabs.panel-default .nav-tabs>li.active>a:hover,
.with-nav-tabs.panel-default .nav-tabs>li.active>a:focus {
  color: #555;
  background-color: #fff;
  border-color: #ddd;
  border-bottom-color: transparent;
}

.with-nav-tabs.panel-default .nav-tabs>li.dropdown .dropdown-menu {
  background-color: #f5f5f5;
  border-color: #ddd;
}

.with-nav-tabs.panel-default .nav-tabs>li.dropdown .dropdown-menu>li>a {
  color: #777;
}

.with-nav-tabs.panel-default .nav-tabs>li.dropdown .dropdown-menu>li>a:hover,
.with-nav-tabs.panel-default .nav-tabs>li.dropdown .dropdown-menu>li>a:focus {
  background-color: #ddd;
}

.with-nav-tabs.panel-default .nav-tabs>li.dropdown .dropdown-menu>.active>a,
.with-nav-tabs.panel-default .nav-tabs>li.dropdown .dropdown-menu>.active>a:hover,
.with-nav-tabs.panel-default .nav-tabs>li.dropdown .dropdown-menu>.active>a:focus {
  color: #fff;
  background-color: #555;
}


/********************************************************************/


/*** PANEL PRIMARY ***/

.with-nav-tabs.panel-primary .nav-tabs>li>a,
.with-nav-tabs.panel-primary .nav-tabs>li>a:hover,
.with-nav-tabs.panel-primary .nav-tabs>li>a:focus {
  color: #fff;
}

.with-nav-tabs.panel-primary .nav-tabs>.open>a,
.with-nav-tabs.panel-primary .nav-tabs>.open>a:hover,
.with-nav-tabs.panel-primary .nav-tabs>.open>a:focus,
.with-nav-tabs.panel-primary .nav-tabs>li>a:hover,
.with-nav-tabs.panel-primary .nav-tabs>li>a:focus {
  color: #fff;
  background-color: #3071a9;
  border-color: transparent;
}

.with-nav-tabs.panel-primary .nav-tabs>li.active>a,
.with-nav-tabs.panel-primary .nav-tabs>li.active>a:hover,
.with-nav-tabs.panel-primary .nav-tabs>li.active>a:focus {
  color: #428bca;
  background-color: #fff;
  border-color: #428bca;
  border-bottom-color: transparent;
}

.with-nav-tabs.panel-primary .nav-tabs>li.dropdown .dropdown-menu {
  background-color: #428bca;
  border-color: #3071a9;
}

.with-nav-tabs.panel-primary .nav-tabs>li.dropdown .dropdown-menu>li>a {
  color: #fff;
}

.with-nav-tabs.panel-primary .nav-tabs>li.dropdown .dropdown-menu>li>a:hover,
.with-nav-tabs.panel-primary .nav-tabs>li.dropdown .dropdown-menu>li>a:focus {
  background-color: #3071a9;
}

.with-nav-tabs.panel-primary .nav-tabs>li.dropdown .dropdown-menu>.active>a,
.with-nav-tabs.panel-primary .nav-tabs>li.dropdown .dropdown-menu>.active>a:hover,
.with-nav-tabs.panel-primary .nav-tabs>li.dropdown .dropdown-menu>.active>a:focus {
  background-color: #4a9fe9;
}


/********************************************************************/


/*** PANEL SUCCESS ***/

.with-nav-tabs.panel-success .nav-tabs>li>a,
.with-nav-tabs.panel-success .nav-tabs>li>a:hover,
.with-nav-tabs.panel-success .nav-tabs>li>a:focus {
  color: #3c763d;
}

.with-nav-tabs.panel-success .nav-tabs>.open>a,
.with-nav-tabs.panel-success .nav-tabs>.open>a:hover,
.with-nav-tabs.panel-success .nav-tabs>.open>a:focus,
.with-nav-tabs.panel-success .nav-tabs>li>a:hover,
.with-nav-tabs.panel-success .nav-tabs>li>a:focus {
  color: #3c763d;
  background-color: #d6e9c6;
  border-color: transparent;
}

.with-nav-tabs.panel-success .nav-tabs>li.active>a,
.with-nav-tabs.panel-success .nav-tabs>li.active>a:hover,
.with-nav-tabs.panel-success .nav-tabs>li.active>a:focus {
  color: #3c763d;
  background-color: #fff;
  border-color: #d6e9c6;
  border-bottom-color: transparent;
}

.with-nav-tabs.panel-success .nav-tabs>li.dropdown .dropdown-menu {
  background-color: #dff0d8;
  border-color: #d6e9c6;
}

.with-nav-tabs.panel-success .nav-tabs>li.dropdown .dropdown-menu>li>a {
  color: #3c763d;
}

.with-nav-tabs.panel-success .nav-tabs>li.dropdown .dropdown-menu>li>a:hover,
.with-nav-tabs.panel-success .nav-tabs>li.dropdown .dropdown-menu>li>a:focus {
  background-color: #d6e9c6;
}

.with-nav-tabs.panel-success .nav-tabs>li.dropdown .dropdown-menu>.active>a,
.with-nav-tabs.panel-success .nav-tabs>li.dropdown .dropdown-menu>.active>a:hover,
.with-nav-tabs.panel-success .nav-tabs>li.dropdown .dropdown-menu>.active>a:focus {
  color: #fff;
  background-color: #3c763d;
}


/********************************************************************/


/*** PANEL INFO ***/

.with-nav-tabs.panel-info .nav-tabs>li>a,
.with-nav-tabs.panel-info .nav-tabs>li>a:hover,
.with-nav-tabs.panel-info .nav-tabs>li>a:focus {
  color: #31708f;
}

.with-nav-tabs.panel-info .nav-tabs>.open>a,
.with-nav-tabs.panel-info .nav-tabs>.open>a:hover,
.with-nav-tabs.panel-info .nav-tabs>.open>a:focus,
.with-nav-tabs.panel-info .nav-tabs>li>a:hover,
.with-nav-tabs.panel-info .nav-tabs>li>a:focus {
  color: #31708f;
  background-color: #bce8f1;
  border-color: transparent;
}

.with-nav-tabs.panel-info .nav-tabs>li.active>a,
.with-nav-tabs.panel-info .nav-tabs>li.active>a:hover,
.with-nav-tabs.panel-info .nav-tabs>li.active>a:focus {
  color: #31708f;
  background-color: #fff;
  border-color: #bce8f1;
  border-bottom-color: transparent;
}

.with-nav-tabs.panel-info .nav-tabs>li.dropdown .dropdown-menu {
  background-color: #d9edf7;
  border-color: #bce8f1;
}

.with-nav-tabs.panel-info .nav-tabs>li.dropdown .dropdown-menu>li>a {
  color: #31708f;
}

.with-nav-tabs.panel-info .nav-tabs>li.dropdown .dropdown-menu>li>a:hover,
.with-nav-tabs.panel-info .nav-tabs>li.dropdown .dropdown-menu>li>a:focus {
  background-color: #bce8f1;
}

.with-nav-tabs.panel-info .nav-tabs>li.dropdown .dropdown-menu>.active>a,
.with-nav-tabs.panel-info .nav-tabs>li.dropdown .dropdown-menu>.active>a:hover,
.with-nav-tabs.panel-info .nav-tabs>li.dropdown .dropdown-menu>.active>a:focus {
  color: #fff;
  background-color: #31708f;
}


/********************************************************************/


/*** PANEL WARNING ***/

.with-nav-tabs.panel-warning .nav-tabs>li>a,
.with-nav-tabs.panel-warning .nav-tabs>li>a:hover,
.with-nav-tabs.panel-warning .nav-tabs>li>a:focus {
  color: #8a6d3b;
}

.with-nav-tabs.panel-warning .nav-tabs>.open>a,
.with-nav-tabs.panel-warning .nav-tabs>.open>a:hover,
.with-nav-tabs.panel-warning .nav-tabs>.open>a:focus,
.with-nav-tabs.panel-warning .nav-tabs>li>a:hover,
.with-nav-tabs.panel-warning .nav-tabs>li>a:focus {
  color: #8a6d3b;
  background-color: #faebcc;
  border-color: transparent;
}

.with-nav-tabs.panel-warning .nav-tabs>li.active>a,
.with-nav-tabs.panel-warning .nav-tabs>li.active>a:hover,
.with-nav-tabs.panel-warning .nav-tabs>li.active>a:focus {
  color: #8a6d3b;
  background-color: #fff;
  border-color: #faebcc;
  border-bottom-color: transparent;
}

.with-nav-tabs.panel-warning .nav-tabs>li.dropdown .dropdown-menu {
  background-color: #fcf8e3;
  border-color: #faebcc;
}

.with-nav-tabs.panel-warning .nav-tabs>li.dropdown .dropdown-menu>li>a {
  color: #8a6d3b;
}

.with-nav-tabs.panel-warning .nav-tabs>li.dropdown .dropdown-menu>li>a:hover,
.with-nav-tabs.panel-warning .nav-tabs>li.dropdown .dropdown-menu>li>a:focus {
  background-color: #faebcc;
}

.with-nav-tabs.panel-warning .nav-tabs>li.dropdown .dropdown-menu>.active>a,
.with-nav-tabs.panel-warning .nav-tabs>li.dropdown .dropdown-menu>.active>a:hover,
.with-nav-tabs.panel-warning .nav-tabs>li.dropdown .dropdown-menu>.active>a:focus {
  color: #fff;
  background-color: #8a6d3b;
}


/********************************************************************/


/*** PANEL DANGER ***/

.with-nav-tabs.panel-danger .nav-tabs>li>a,
.with-nav-tabs.panel-danger .nav-tabs>li>a:hover,
.with-nav-tabs.panel-danger .nav-tabs>li>a:focus {
  color: #a94442;
}

.with-nav-tabs.panel-danger .nav-tabs>.open>a,
.with-nav-tabs.panel-danger .nav-tabs>.open>a:hover,
.with-nav-tabs.panel-danger .nav-tabs>.open>a:focus,
.with-nav-tabs.panel-danger .nav-tabs>li>a:hover,
.with-nav-tabs.panel-danger .nav-tabs>li>a:focus {
  color: #a94442;
  background-color: #ebccd1;
  border-color: transparent;
}

.with-nav-tabs.panel-danger .nav-tabs>li.active>a,
.with-nav-tabs.panel-danger .nav-tabs>li.active>a:hover,
.with-nav-tabs.panel-danger .nav-tabs>li.active>a:focus {
  color: #a94442;
  background-color: #fff;
  border-color: #ebccd1;
  border-bottom-color: transparent;
}

.with-nav-tabs.panel-danger .nav-tabs>li.dropdown .dropdown-menu {
  background-color: #f2dede;
  /* bg color */
  border-color: #ebccd1;
  /* border color */
}

.with-nav-tabs.panel-danger .nav-tabs>li.dropdown .dropdown-menu>li>a {
  color: #a94442;
  /* normal text color */
}

.with-nav-tabs.panel-danger .nav-tabs>li.dropdown .dropdown-menu>li>a:hover,
.with-nav-tabs.panel-danger .nav-tabs>li.dropdown .dropdown-menu>li>a:focus {
  background-color: #ebccd1;
  /* hover bg color */
}

.with-nav-tabs.panel-danger .nav-tabs>li.dropdown .dropdown-menu>.active>a,
.with-nav-tabs.panel-danger .nav-tabs>li.dropdown .dropdown-menu>.active>a:hover,
.with-nav-tabs.panel-danger .nav-tabs>li.dropdown .dropdown-menu>.active>a:focus {
  color: #fff;
  /* active text color */
  background-color: #a94442;
  /* active bg color */
}
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<link href="//netdna.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css" rel="stylesheet" id="bootstrap-css">
<script src="//netdna.bootstrapcdn.com/bootstrap/3.2.0/js/bootstrap.min.js"></script>
<!------ Include the above in your HEAD tag ---------->

<div class="container">
  <div class="page-header">
    <h1>Panels with nav tabs.<span class="pull-right label label-default">:)</span></h1>
  </div>
  <div class="row">
    <div class="col-md-6">
      <div class="panel with-nav-tabs panel-default">
        <div class="panel-heading">
          <ul class="nav nav-tabs">
            <li class="active"><a href="#tab1default" data-toggle="tab">Default 1</a></li>
            <li><a href="#tab2default" data-toggle="tab">Default 2</a></li>
            <li><a href="#tab3default" data-toggle="tab">Default 3</a></li>
            <li class="dropdown">
              <a href="#" data-toggle="dropdown">Dropdown <span class="caret"></span></a>
              <ul class="dropdown-menu" role="menu">
                <li><a href="#tab4default" data-toggle="tab">Default 4</a></li>
                <li><a href="#tab5default" data-toggle="tab">Default 5</a></li>
              </ul>
            </li>
          </ul>
        </div>
        <div class="panel-body">
          <div class="tab-content">
            <div class="tab-pane fade in active" id="tab1default">Default 1</div>
            <div class="tab-pane fade" id="tab2default">Default 2</div>
            <div class="tab-pane fade" id="tab3default">Default 3</div>
            <div class="tab-pane fade" id="tab4default">Default 4</div>
            <div class="tab-pane fade" id="tab5default">Default 5</div>
          </div>
        </div>
      </div>
    </div>
    <div class="col-md-6">
      <div class="panel with-nav-tabs panel-primary">
        <div class="panel-heading">
          <ul class="nav nav-tabs">
            <li class="active"><a href="#tab1primary" data-toggle="tab">Primary 1</a></li>
            <li><a href="#tab2primary" data-toggle="tab">Primary 2</a></li>
            <li><a href="#tab3primary" data-toggle="tab">Primary 3</a></li>
            <li class="dropdown">
              <a href="#" data-toggle="dropdown">Dropdown <span class="caret"></span></a>
              <ul class="dropdown-menu" role="menu">
                <li><a href="#tab4primary" data-toggle="tab">Primary 4</a></li>
                <li><a href="#tab5primary" data-toggle="tab">Primary 5</a></li>
              </ul>
            </li>
          </ul>
        </div>
        <div class="panel-body">
          <div class="tab-content">
            <div class="tab-pane fade in active" id="tab1primary">Primary 1</div>
            <div class="tab-pane fade" id="tab2primary">Primary 2</div>
            <div class="tab-pane fade" id="tab3primary">Primary 3</div>
            <div class="tab-pane fade" id="tab4primary">Primary 4</div>
            <div class="tab-pane fade" id="tab5primary">Primary 5</div>
          </div>
        </div>
      </div>
    </div>
  </div>
</div>
<div class="container">
  <div class="row">
    <div class="col-md-6">
      <div class="panel with-nav-tabs panel-success">
        <div class="panel-heading">
          <ul class="nav nav-tabs">
            <li class="active"><a href="#tab1success" data-toggle="tab">Success 1</a></li>
            <li><a href="#tab2success" data-toggle="tab">Success 2</a></li>
            <li><a href="#tab3success" data-toggle="tab">Success 3</a></li>
            <li class="dropdown">
              <a href="#" data-toggle="dropdown">Dropdown <span class="caret"></span></a>
              <ul class="dropdown-menu" role="menu">
                <li><a href="#tab4success" data-toggle="tab">Success 4</a></li>
                <li><a href="#tab5success" data-toggle="tab">Success 5</a></li>
              </ul>
            </li>
          </ul>
        </div>
        <div class="panel-body">
          <div class="tab-content">
            <div class="tab-pane fade in active" id="tab1success">Success 1</div>
            <div class="tab-pane fade" id="tab2success">Success 2</div>
            <div class="tab-pane fade" id="tab3success">Success 3</div>
            <div class="tab-pane fade" id="tab4success">Success 4</div>
            <div class="tab-pane fade" id="tab5success">Success 5</div>
          </div>
        </div>
      </div>
    </div>
    <div class="col-md-6">
      <div class="panel with-nav-tabs panel-info">
        <div class="panel-heading">
          <ul class="nav nav-tabs">
            <li class="active"><a href="#tab1info" data-toggle="tab">Info 1</a></li>
            <li><a href="#tab2info" data-toggle="tab">Info 2</a></li>
            <li><a href="#tab3info" data-toggle="tab">Info 3</a></li>
            <li class="dropdown">
              <a href="#" data-toggle="dropdown">Dropdown <span class="caret"></span></a>
              <ul class="dropdown-menu" role="menu">
                <li><a href="#tab4info" data-toggle="tab">Info 4</a></li>
                <li><a href="#tab5info" data-toggle="tab">Info 5</a></li>
              </ul>
            </li>
          </ul>
        </div>
        <div class="panel-body">
          <div class="tab-content">
            <div class="tab-pane fade in active" id="tab1info">Info 1</div>
            <div class="tab-pane fade" id="tab2info">Info 2</div>
            <div class="tab-pane fade" id="tab3info">Info 3</div>
            <div class="tab-pane fade" id="tab4info">Info 4</div>
            <div class="tab-pane fade" id="tab5info">Info 5</div>
          </div>
        </div>
      </div>
    </div>
  </div>
</div>
<div class="container">
  <div class="row">
    <div class="col-md-6">
      <div class="panel with-nav-tabs panel-warning">
        <div class="panel-heading">
          <ul class="nav nav-tabs">
            <li class="active"><a href="#tab1warning" data-toggle="tab">Warning 1</a></li>
            <li><a href="#tab2warning" data-toggle="tab">Warning 2</a></li>
            <li><a href="#tab3warning" data-toggle="tab">Warning 3</a></li>
            <li class="dropdown">
              <a href="#" data-toggle="dropdown">Dropdown <span class="caret"></span></a>
              <ul class="dropdown-menu" role="menu">
                <li><a href="#tab4warning" data-toggle="tab">Warning 4</a></li>
                <li><a href="#tab5warning" data-toggle="tab">Warning 5</a></li>
              </ul>
            </li>
          </ul>
        </div>
        <div class="panel-body">
          <div class="tab-content">
            <div class="tab-pane fade in active" id="tab1warning">Warning 1</div>
            <div class="tab-pane fade" id="tab2warning">Warning 2</div>
            <div class="tab-pane fade" id="tab3warning">Warning 3</div>
            <div class="tab-pane fade" id="tab4warning">Warning 4</div>
            <div class="tab-pane fade" id="tab5warning">Warning 5</div>
          </div>
        </div>
      </div>
    </div>
    <div class="col-md-6">
      <div class="panel with-nav-tabs panel-danger">
        <div class="panel-heading">
          <ul class="nav nav-tabs">
            <li class="active"><a href="#tab1danger" data-toggle="tab">Danger 1</a></li>
            <li><a href="#tab2danger" data-toggle="tab">Danger 2</a></li>
            <li><a href="#tab3danger" data-toggle="tab">Danger 3</a></li>
            <li class="dropdown">
              <a href="#" data-toggle="dropdown">Dropdown <span class="caret"></span></a>
              <ul class="dropdown-menu" role="menu">
                <li><a href="#tab4danger" data-toggle="tab">Danger 4</a></li>
                <li><a href="#tab5danger" data-toggle="tab">Danger 5</a></li>
              </ul>
            </li>
          </ul>
        </div>
        <div class="panel-body">
          <div class="tab-content">
            <div class="tab-pane fade in active" id="tab1danger">Danger 1</div>
            <div class="tab-pane fade" id="tab2danger">Danger 2</div>
            <div class="tab-pane fade" id="tab3danger">Danger 3</div>
            <div class="tab-pane fade" id="tab4danger">Danger 4</div>
            <div class="tab-pane fade" id="tab5danger">Danger 5</div>
          </div>
        </div>
      </div>
    </div>
  </div>
</div>
<br/>