"We are happy with the winning start and the three points but obviously we could have scored much earlier and it may have turned out to be an easier game than it was," said captain Philipp Lahm.
"We had huge chances in the first half and over 90 minutes we had the far better opportunities to score."
Bayern needed a 90th minute goal from defender Jerome Boateng after they saw City keeper Joe Hart deny them on several occasions despite dominating the game and having close to 60 percent possession.
Apart from Hart, they also had their own finishing to blame for not taking an earlier lead with Thomas Mueller and Lewandowski, among other, firing into the side-netting from close range.
In their defence, a string of injuries have contributed to the Bavarians still looking for last season's explosiveness that led them to the domestic league and Cup double.
Winger Franck Ribery and playmaker Bastian Schweinsteiger are still out injured and while new transfers Xabi Alonso and Mehdi Benatia add confidence at the back, their front line is still far from peaking.
World Cup fatigue among many of the Bayern players has also played its role in their less-than-spectacular start as well as the absences of Thiago Alcantara, Javi Martinez and Holger Badstuber through injuries.
"Not everything was super today but we fought until the end and we were then rewarded," scorer Boateng said.
The introduction of Dutch winger Arjen Robben, who had also been out injured for a few weeks, late in the game of Wednesday instantly added spark and pace down the wings and it was a move he started that eventually led to Boateng's winner.
It should be a different picture once coach Pep Guardiola has a full fit squad to choose from and Lewandowski breaks his goal drought with Roma and CSKA Moscow also in their Champions League group.
"What is very positive is that we carved out that many scoring chances," said Robben. "I think we are on the right track."
(This story was refiled to correct typo in intro)
(Editing by Amlan Chakraborty)
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