England goalkeeper Hart produced a string of superb saves in Wednesday's Group E opener at the Allianz Arena and his heroics looked to have secured a goalless draw against the Bundesliga champions.
Bayern were not to be denied, though, as Hart was finally beaten by an 89th-minute strike from former City defender Jerome Boateng via a deflection off Mario Gotze.
City were second best for much of the game, but Hart thought the Premier League champions were worthy of a point after thwarting Bayern until the game took a late twist.
"We fought hard all night against a good team you know what you get when you come here," he told Sky Sports.
"A nasty deflection at the end has done us and Jerome Boateng comes back to haunt us. It would have been a well-deserved draw, we made them work hard for everything. I tend to be busy against German teams."
City face Roma, who hammered CSKA Moscow 5-1 on Wednesday, at the Etihad Stadium in their second pool clash at the end of this month and Hart is in no doubt they can respond to their defeat in Munich to qualify.
He added: "We can match Bayern Munich, we have some very tough games and we have to play well against CSKA and Roma now. We're confident we can win the rest of our games."
