The National League Stones ultimately came up short at home to League Two Oldham.
A first-half error from Alex Finney proved to be the turning point as Athletic secured a 2-0 victory to take a third round place.
But despite a self-inflicted wound, Wheeler didn’t feel disappointed.
“They gave it their all and that’s all I can ask of them,” said the manager, who turned his attention to survival after poor league run.
“We went toe-to-toe with them for most of the match - it’s all about fine lines and we’ve not been able get that little bit of luck.
“We were missing a number of important players and in the FA Cup against League sides you need everyone - and everyone firing.
“It wasn’t to be but they gave me everything. I don’t think we were second best.”
Maidstone travel to Barrow next in the National League before a game with Woking in the FA Trophy.