Hart has kept his place for club and country despite patchy form so far this season, helping England secure their place in next summer's World Cup finals with Wembley wins over Montenegro and Poland.
Pellegrini has admitted that Hart's struggles in last month's Champions League defeat to Manchester City were the "worst moments" of the stopper's career, but remains adamant that he was right to retain him as the club's number one.
He told The Mirror: "I think both England games, for him, were very, very important. He was in his worst moment before the two international games.
"I think that he showed that he has the personality to do well, even in his worst moments. I suppose he will improve in confidence, and all of us trust him. It was a very difficult game for him.
"But I'm sure that I made the right decision to keep him, and Joe showed me it was the best decision."
City are back in Premier League action tomorrow, looking to earn their first away win of the campaign against West Ham United.