Hart gave a solid performance against Everton before helping England secure qualification for next summer's World Cup, notably keeping Poland's Robert Lewandowski at bay on Tuesday night.
Pellegrini believes Hart's ability to raise his game even when under pressure marks him out, and the Chilean has backed the goalkeeper to gain confidence from his international displays.
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"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.
"I am sure that I made the right decision to keep him and Joe showed me it was the best decision."
Along with Hart, a number of City's players helped their nations secure a place at Brazil next summer, and Pellegrini hopes the motivation to secure a World Cup spot could help their campaign.
"I think, for the players, it's very important they qualify for the World Cup," the former Malaga boss added.
"I think it's the most important thing in football so all of them that have are very happy. And of course they all want to arrive in their best form for the World Cup."