Bayern, who lost 4-2 to rivals Borussia Dortmund in the German Super Cup last week, take on lower-tier SW Rehden in the German Cup first round on Monday.
"We played a good first half but did not attack enough," Bayern's new coach Pep Guardiola told reporters.
"Obviously City are a very strong team. With some substitutions in the second it worked better. I am optimistic for the season. The coach always has to be optimistic."
Despite dominating much of the game, Bayern, who won the Champions League as well as the domestic double last season, found themselves trailing on the hour.
New City signing Alvaro Negredo latched on to a Samir Nasri pass to beat Javi Martinez in a sprint and slot past keeper Manuel Neuer on the hour.
The Premier League side's joy was short-lived though as man-of-the-match Thomas Mueller converted a penalty awarded for handball five minutes later and the hosts added another with a low header from Mario Mandzukic in the 73rd.
Bayern, who beat Sao Paolo 2-0 on Wednesday to reach the four-team mini tournament final, have looked sharper this week with Spaniard Guardiola saying he was impressed by how quickly his players were adopting "my very small ideas."
City had beaten AC Milan 5-3 on Wednesday.
"We are on a good level, but you saw today that we still have some problems at the back," Mueller told reporters. "We still have room for improvement.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
