There were doubts over the 26-year-old's position after he was culpable for two of Bayern Munich's goals in City's Champions League defeat on Wednesday.
The City stopper got his hand to Romelu Lukaku's shot in the 16th minute but could not keep it out.
Pellegrini did not blame Hart, saying: "Always the responsibility for the goal is with the whole team."
But asked about his decision to choose Hart ahead of Costel Pantilimon, Pellegrini said: "It wasn't a simple decision, it was a very difficult decision, but I think Joe needs the trust of all of us - of me, the other players and the fans.
"Of course he feels he didn't do well the last game, he feels that he was guilty, but it was more important that today he reflected how strong his character is."
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