The goalkeeper came under fire following the Champions League Group D fixture after first fumbling Franck Ribery's 25-yard effort for the visitors' opener before being beaten easily at his near post by Arjen Robben for the third goal.
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"Of course I am worried about the mistakes," the City boss told reporters. "[But] the three goals, I think we can do better, not only the goalkeeper."
Hart's team-mate Micah Richards also faced scrutiny after enduring a torrid evening against Ribery.
His inclusion ahead of Pablo Zabaleta at full-back was a surprise for some, but Pellegrini exonerated the 25-year-old of blame.
He added: "I don't think Ribery was the key factor to win the game.
"I don't think Micah Richards has the responsibility - the same as all the other players, but I don't think he has any special problems."
Pellegrini's side have now suffered back-to-back defeats, with the Bayern setback following a 3-2 reverse to Aston Villa last Saturday.