The Bavarian giants required a stunning 90th-minute strike from ex-City defender Jerome Boateng to settle the Group E contest in Munich on Wednesday.
City started brightly but could not find a way through a stubborn Bayern defence at the Allianz Arena.
Guardiola tinkered things to cope with the Premier League side's presence out wide and saw his side improve before Boateng fired into the top-right corner in the dying stages.
"We played really well but in the first 20 minutes, Manchester City were the better team," Guardiola said afterwards.
"We started with four players in our defence because I knew that City planned to stay really close on the byline with [Samir] Nasri and [Jesus] Navas, especially Navas.
"Nevertheless we couldn't dominate the game. We had a lot of problems with Nasri and Navas.
"After 20 minutes we changed the system, with two players in the middle and after that we played much better.
"In the last 15 minutes of the second half we dominated the game - we created a lot of chances, but it's not easy against Manchester City.
"We played with passion [though] and that's why we earned this win today."
Roma thrashed CSKA Moscow 5-1 in the other Group E clash to leave City behind the eight-ball already.
And Guardiola acknowledged just how important victory in Bayern's first group match was, given the highly competitive pool.
"We know how difficult this group is and we know it will go down to the last game here against CSKA Moscow but this victory and this start is very important to us," he added.
"The UEFA Champions League is really difficult. If we lost today it would have been really hard.
"My humble opinion is that there are six or seven teams that can win the Champions League. City are one of them. Against this opponent, three points is really important."
