City enjoyed much of the early possession but lacked the killer touch in front of goal.
Despite the home side's early dominance, Bayern posed a constant threat on the break and could have taken the lead when Ivica Olic's shot was saved at the near post by Joe Hart.
The hosts had the ball in the net soon after, when David Silva's free kick evaded everyone to fly in. However, a foul was given after Joleon Lescott was adjudged to have barged the goalkeeper.
Silva's next effort was given as the Spaniard fired in from 20 yards with 36 minutes on the clock.
Roberto Mancini's team came flying out of the traps after the break and soon doubled their lead when Yaya Toure's run ended with the Ivorian poking the ball into the far corner.
Despite City's endeavour, Napoli's win at Villarreal has meant that the English side will not be in the knockout stages of the competition.