Pellegrini picked up his first trophy as City manager on Sunday with a 3-1 win over Sunderland in the League Cup final at Wembley.
With City still in the running for the domestic title as well as the FA Cup and UEFA Champions League, Pellegrini believes silverware will keep the players' trust and help the club to improve further.
"I think when the players have more confidence, more trust in the way they must do things, I'm absolutely sure that this club will continue improving," he told The National.
"That's why it's so important to win the title, to win something important this year, because the only way that the players will trust in what we're doing is by winning.
"The work in this team is just starting, the owner has had just four years here, the philosophy of the club in those four years has been taking shape and I hope this will remain the same in the future, with or without me.
"The manager of the first team must use the same philosophy across the whole academy. We will have a way of developing our young players who will be very useful for us in the future."
City can move a step closer to winning an unprecedented quadruple when Pellegrini's men take on last season's FA Cup final foes Wigan Athletic in the quarter-finals this weekend.
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