Chelsea came from 1-0 down at halftime to win 4-1 in Wroclaw on Thursday night. The result saw Chelsea become the first club to win every UEFA trophy.
Colwill said afterwards: "To be the first club to have won everything possible, you can see the fans celebrating now and it shows how much it means to them.
"We knew they were going to be a good team, especially at the start with their fans pushing them on, but we knew it was going to die off. We just had to wait and pick our moments and that is what we did in the second half.
"Watching from the bench you can see where the spaces are and how you can help the team. When I came on for Benny (Badiashile) I could see he was working so hard and then the gaps were open. He did that for me, laid the foundations for me."
An amazing week
Chelsea win the ECL in the same week they clinched Champions League qualification with victory at Nottingham Forest.
Colwill added: "It has been amazing.
"We have achieved everything we wanted to do. It feels amazing winning my first European competition with Chelsea, hopefully many more to go. And getting Champions League for next season, I don't think you can get any better than that."