The Indo-French combination proved to be no match to Austria's Oliver Marach and Fabrice Martin of France, going down 2-6 4-6.
The Austrian-French pair will now face the American duo of Scott Lipsky and Eric Butorac in the quarter-finals.
In the opening set, Paes and Chardy suffered an early blow as their serve was broken in the third game itself. They failed to recover from there on, even as Marach and Martin managed to clinch another break of serve in the seventh game before serving out the set.
The Austrian-French duo capitalised on the advantage and comfortably wrapped up the match in their favour.