The goal and the result saw Chelsea clinch Champions League qualification ahead of Forest.
Colwill said afterwards: "When I scored, I stayed calm because we still had more minutes to play but I stayed calm and helped the boys.
"What I got taught in the academy is you have to fight. We try to get these clean sheets to win and that's what we did today.
"We had to win. We knew we had to win and that it wasn't going to be a hard atmosphere but we did it.
"This club deserves to be in the Champions League."
So many said we wouldn't make it
Meanwhile, Blues skipper Reece James also said: "It is an amazing feeling.
"We knew coming here on the final day would be tough. They have had an amazing season - they have so much threat going forward.
"We had to dig in. We both needed to win, but I am so happy that the team got the job done today.
"We talk about being the best team-mate and everybody showed that today.
"So many people before the season, during the season had disbelief - they told us 'we were you young, inexperienced and were not going to make it'. But we are here."