Pellegrini, who was appointed on June 14, secured his first piece of silverware following City's 1-0 win over Sunderland in the Asia Trophy final on Saturday.
Stevan Jovetic, Alvaro Negredo, Fernandinho and Jesus Navas have all moved to Eastlands in the close-season as City ready themselves to try to claim back the Premier League title from rivals Manchester United.
And Kompany, 27, is excited by Pellegrini's "vision" for the club.
"We’ve had a lot of good things in our team. Our organisation and discipline has been really good," Kompany told the Manchester Evening News.
"(Pellegrini) has got his own vision and I think like every big manager he's got a strong vision about how the team needs to play.
"I think what he’s trying to do is add on to what we have already and just make sure that those little points that we could improve we do improve, maybe recovering the ball quicker and being more dynamic."
The Belgium international has been at City since 2008 after being recruited by then-manager Mark Hughes and played a key part as the club won their first title since 1968 in 2012.
Having finished 11 points behind champions United last season, Kompany is relishing the start of the upcoming campaign on August 19 against Newcastle United.
"When you finish second and everyone’s disappointed. That’s a good thing because a few years ago people might have been happy with that," he added.
"I think this squad is just as strong, if not stronger, than the squad that gave us the league title."
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