Coach Jupp Heynckes and his players were happy to banish the nightmares of losing last season's final to Chelsea in Munich but agreed their display against the Spanish team was far from their best.
"There is still room for improvement for the entire team," said Heynckes after watching his players dominate the Spanish side throughout but failing to shut out the game early on.
A first half goal by Bastian Schweinsteiger created only a fragile lead and did little to hide sloppy defending and less-than-clinical finish up front.
With Valencia huddled in their own half, the Germans should have added several more goals but failed to convert a string of chances.
Toni Kroos did eventually add another for the hosts late in the game but a concentration lapse saw them concede a goal in stoppage time.
Nelson Valdez was almost unchallenged when he rose at the heart of the Bayern defence above two players to head in. Had he scored earlier, it could have turned out to be a very jittery game for the Germans.
Bayern then were awarded a stoppage time penalty for a foul on Arjen Robben but again they fumbled with Mario Mandzukic driving a weak spot kick into the arms of the Valencia keeper.
"The final phase of the game was unsatisfactory. When you lead 2-0 you cannot let your guard down and it is equally annoying that we do not take full advantage of the penalty," said Heynckes.
With their top striker Mario Gomez, who notched 12 goals in the Champions League last season, and sensational midfielder David Alaba still injured and wingers Arjen Robben and Franck Ribery only back from minor injuries, Bayern can expect to grow stronger as the competition continues.
Maintaining control of the Bundesliga which they lead with maximum points from three games will be equally confidence-boosting for the Bavarians, who have domestically played second fiddle to champions Borussia Dortmund in the past two seasons.
"The goal we let in was unnecessary and we should have scored a second goal much earlier," said captain Philipp Lahm. "But at the end of the day we took three points and it was a good start against the toughest opponent in the group."
Bayern top Group F along with BATE Borisov who stunned hosts Lille 3-1 in their opener on Wednesday.
"This is a new season and a new chance for us and we start again from scratch," said Arjen Robben. "Everyone is motivated and hungry for success. We can start building on this 2-1 win."
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