Hart was at fault for two of Bayern's three goals during City's defeat, but Pellegrini has reassured the England stopper that he has the trust of his teammates.
The 60-year-old told reporters: "He feels that he didn't do very well, but I don't think that there is any problem.
"He continues with the trust of all of the team, so we hope that he recovers from what happened in the last match.
"Joe knows that he must improve, but he also knows that he has our trust."
Pellegrini would not disclose whether Hart would retain his place in the starting lineup for their match with Everton on Saturday.