Robert Lewandowski and Corentin Tolisso secured a 2-1 success at the Constant Vanden Stockstadion, but Jupp Heynckes' men rode their luck for large parts.
Anderlecht's equaliser through Sofiane Hanni was their first Champions League goal of the season, hinting that the Belgians' profligacy, rather than Bayern's backline, was key.
Bayern have slim hopes of topping Group B with a game to play, but they must overturn a three-goal deficit to Paris Saint-Germain while beating the pool leaders on the final matchday.
Carlo Ancelotti was sacked following the 3-0 loss at Parc des Princes, but Boateng pegged Wednesday's performance as worse than anything they have offered up for some time.
He said: "I think everyone saw that we played really bad in the first half. One of the worst matches for a long time.
"We couldn't get used to the pitch, made too many errors, weren't aggressive, weren't compact.
"Every one of us has to ask ourselves what kind of a half that was and we can thank Sven Ulreich that we weren't behind at the half.
"The second half was much better, we kept the ball. But in the last minutes we did the same thing we did in the first half."
PSG are the top scorers in the competition, with 24 goals scored in five games and Celtic striker Moussa Dembele's opener in Wednesday's 7-1 Paris thrashing was the first goal Unai Emery's side have conceded in the Champions League this term.
"When we have a chance [for first place in the group], we always have to try," Lewandowski added.
"Sure, we have to win 4-0. It will be difficult, but in Munich in the Allianz Arena anything can happen. As long as there is a chance, we will try and we will give it everything we got."