Ignore citations in captions in list of figures when numbering

This exact problem is solved by the notoccite package written by Donald Arsenau.

I have found it throught the worth reading bibtex faq: http://mirrors.ctan.org/biblio/bibtex/contrib/doc/btxFAQ.pdf (see question 18).

Use the optional argument of \caption:

\caption[<Figure title>]{<Figure title> \cite{<Source>}}

EDIT: You'd "still like the citation to appear in the caption in the listoffigures but just to have the number as if it were from it's position in the main body of text". I don't know how to do this using the ieeetr style, but it works out of the box using biblatex:

\documentclass{article}

\usepackage[sorting=none]{biblatex}

\usepackage{filecontents}

\begin{filecontents}{\jobname.bib}
@misc{A01,
  author = {Author, A.},
  year = {2001},
  title = {Alpha},
}
@misc{B02,
  author = {Buthor, B.},
  year = {2002},
  title = {Bravo},
}
\end{filecontents}

\addbibresource{\jobname.bib}

\begin{document}

\listoffigures

\section{foo}

Some text \autocite{B02}.

\begin{figure}[!h]
\centering
\rule{1cm}{1cm}
\caption{A figure \autocite{A01}}
\end{figure}

\printbibliography

\end{document}