Colwill helped Chelsea to a clean sheet as the hosts 1-0 thanks to a 50th minute strike from Enzo Fernandez.
He told Sky Sports: "It was a tough one out there but it meant everything to me, the boys and the fans, especially. The fans were amazing out there. they got us through that I can tell you that.
"It was giving the Tottenham fans stick and that was what we needed. That gave us the extra 10 minutes, the runs at the end and the boys were buzzing from it. That was amazing.
"We felt comfortable. We knew how they play and we knew how to hurt them. Today we played really well and we could've scored way more chances.
"Everyone always says I have a load of potential but I don't think potential means anything, you've got to show it every game. This season, at times, I have at times I haven't. I need to keep progressing and learning because I know where I can be and under this gaffer he'll take me there I'm sure.
"We need to win games at the end of the day. we're fighting for Champions League. To win games we have to change style sometimes. We knew they have a high line and we have Nicolas Jackson. He's a huge threat, to feet and in behind and we know if we play to his advantages we'll score goals and today we did score goals through that."