Chelsea finished the season as Club World Cup and Europa Conference League winners, along with Champions League qualifiers.
Reflecting on the campaign, Colwill 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."
On the Club World Cup, Colwill added: "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 he future. I think we're ready and we'll see next season."