The goalkeeper fumbled Franck Ribery's opener for Bayern Munich before being caught out at his near post for the third goal, and the Manchester City boss is worried by the errors
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.