Bayern were trailing 2-1 entering the final two minutes of the clash at Signal Iduna Park, but an own goal from Dortmund defender Lukasz Piszczek saw the scores levelled, before Bayern won the resulting penalty shootout 5-4.
Carlo Ancelotti's side entered the match off the back of a difficult pre-season, but Lewandowski is confident that his team 'will be perfect in a few months'.
"I'm very glad about the victory, it is the first title," Lewandowski told Bayern's official website. "We turned in a very good display. We made a few mistakes but it is the first match of the season.
"We have to step it up even more now. I'm sure everything will be going perfectly in a few months. We will surely be as strong as in the last or the second-to-last year. It was a different kind of preparation for us, but now we had a little more time to train, and I'm very happy that we won the first title."
Next up for Bayern is a clash with third-tier side Chemnitzer in the DFB-Pokal on Saturday.