The 26-year-old England goalkeeper revealed Pellegrini's methods are 'easier' to understand than those of his predecessor, Roberto Mancini.
Hart told the Manchester Evening News: "It's going well. 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. It sounds strange but I stand in goal and I don't know that much about football management.
"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. There's a few of us who have stayed but we know our goals whoever is in charge. I think it should work out. We've got some good players here and hopefully we'll do some good things this season."