Pellegrini was appointed as Roberto Mancini's successor in June and Hart has hinted the Chilean's methods are easier to understand than those of the Italian.
City have experienced an indifferent pre-season campaign, with a 5-3 victory over AC Milan in the Audi Cup a highlight, but the 26-year-old goalkeeper is confident the former Premier League champions are well set for a successful season.
"It's going well," he told the Manchester Evening News. "We know where we stand and how he wants us to play. It worked for the first half an hour against Milan but then it all fell a part a bit.
"We're going in the right direction and it feels good.
"In terms of how I feel about him [Pellegrini], he seems very direct in what he wants and what he needs and that's a lot easier to deal with as a player.
"There's different staff and different players. I think it should work out. We've got some good players here and hopefully we'll do some good things this season."
Hart was again an ever-present player in the Premier League last season for the third campaign running, but will be hoping to eradicate the errors that began to creep into his game and drew criticism from Mancini.