Bayern jumped into a 2-0 lead through Thomas Muller and Mario Gotze inside the first 12 minutes.
David Silva pulled a goal back before half-time before an Aleksandar Kolarov penalty and Milner's 62nd-minute strike completed an unlikely comeback.
While City were unable to push on for another goal which would have seen them displace Bayern at the top of the group, Milner felt there were a lot of positives to take from the game.
The midfielder believes that City showed they have the quality and desire to make an impact in the knockout stages.
"It says a lot about the dressing-room and the character of the players," he told Sky Sports.
"It was a terrible start and we gave away some sloppy goals.
"But to go to a place like this and go 2-0 down and then come back and win shows the character in this dressing-room.
"It was not enough to win the group but it shows the type of performance we need in the next round. We can come to a place like this and score goals.
"We wanted a bit of revenge after the first game (which City lost 3-1). It will give us a lot of belief.
"We will come up against a good team like Bayern (in the next round)."