The Poland international's wait for a first competitive goal extended to 259 minutes on Friday as he was unable to beat Wolfsburg goalkeeper Max Grun at the Allianz Arena.
Grun denied the 26-year-old on numerous occasions, including an impressive save when Lewandowski only had him to beat.
Despite the striker's misses, his side got off to a winning start as Arjen Robben and Thomas Muller secured a 2-1 win and a fine start to their Bundesliga title defence.
Lewandowski, who was substituted with 11 minutes to go, expects to keep improving as he settles into life at Bayern and is sure he will be contributing goals to their cause before long.
"We won our first match and picked up our first three points," he said. "I hope the next match will be even better and of course I hope I can score.
"I think I have never scored in my first match. I had two good chances but I think I'll do better next week.
"Of course a goal would have been good for me but I'm not upset. We have three points. I have to stay calm, but I'm sure I'll score soon."
His next chance to open his account on Saturday when they visit Schalke in the Bundesliga.
