If we use potentiometers as volume controls, don't they waste electric power?

If you do this, then it will waste a lot of power:

^{simulate this circuit – Schematic created using CircuitLab}

You'll also need a very large and heavy potentiometer because it will have to handle all the power that the speaker can handle.

If you do this, then almost no power will be wasted:

^{simulate this circuit}

The signal is very low power, and you only waste a tiny bit of that tiny bit by varying the volume. The potentiometer can also be small because it only has to handle a tiny little bit of power.

\$\color{red}{\boxed{\text{Will it waste electrical energy?}}}\$

Potentiometers are variable resistors and resistors waste power: -

$$P_{dissipation} = \dfrac{V_{applied}^2}{R}$$

Or

$$P_{dissipation} = I_{applied}^2\cdot R$$

Power wasted is also energy wasted if you regard heat as a waste product.

If we use potentiometers as volume controls, don't they waste electric power?

Yes.

I recently heard that we use potentiometers to reduce the volume levels in audio devices. Will it waste electrical energy?

Anything resistive is going to waste power to a certain degree, however in audio amplifier applications a potentiometer is used to control the gain of the amplifier.

If memory serves me correctly:

You can think of an amplifier as a black box with a set of input/outputs, such described like this; High Voltage input, High Voltage outputs and pre-input stage side/control stage(LV).

The control of the volume is done by changing the resistance of the feedback circuit in the amplifier. The feedback circuit determines the level of gain/voltage allowed on the output. It is set by a series of resistors. The potentiometer is one part that can vary its resistance, and hence vary the gain of the amplifier circuit.

It all goes back to how a transistor fundamentally works, where a small current on the input can open a higher potential side of the transistor, via the changing the conduction properties of the junction layer via micro currents. Think of it as valve letting out water from a giant dam, it takes no effort to open the valve vs the energy expended by the water flowing. Do this fast enough and you can modulate a high power output via small input, in this case the amount of water flowing (voltage) over a given time.