Highly unlikely. If so, we did a fantastic job of destroying/hiding each and every piece of evidence to suggest that there was a civilization there before we left.
The idea of a civilization on Mars has its roots with the astronomer Percival Lowell, who thought that he could make out canals on the surface of Mars with the use of his relatively low resolution (not at the time, but it is now) telescope, and with this he came up with elaborate stories about a dying civilization using the last of its resources to attempt to tap the water held on Mars' poles.
Later, when we imaged the planet more thoroughly through the use of probes we found no canals, merely natural surface features and crags, which were not nearly as geometric as Lowell and others thought they were. The features that he thought he saw are now pretty much universally recognized to be a result of human error by astronomers,
Nevertheless, the myth still persists in popular culture.