The Blues lifted the Club World Cup after beating PSG 3-0 in the final of the revamped competition at the weekend and the defender is confident that the club can build on their success next season.
Colwill said: "I said at the start of this tournament that our plan is to win it [Club World Cup] and people looked at me as if I was crazy.
"So I'm going to say the exact same thing now going into the Premier League and Champions League.
"This is the biggest trophy I've ever won. I think the Club World Cup will be bigger than the Champions League and we were the first team to win it.
"It was a statement victory and, in the future, if we keep winning trophies then everyone will give us the love that we deserve. But we'll only know that in the future. I think we're ready and we'll see next season."
Chelsea have undergone a period of wholesale change since co-owner Todd Boehly arrived at Stamford Bridge in 2022 but Colwill is confident that the team can emulate the great Blues sides of the past.
He said: "We're a team and that's in the Chelsea identity. You stick together no matter what. I think players like John Terry, Frank Lampard, Didier Drogba, they started that and we're carrying it on.
"They were all amazing players, the best players who won a lot but we've got the best players in our team - young players for sure - and that's our plan, to win the biggest trophies for Chelsea.
"We're definitely capable of doing it. I think we've shown that. Everyone said that PSG were the best team in the world but we won 3-0."