The U's ended a run of six games without a win with a narrow victory over the Sky Blues, to move four points above the relegation zone.
Colchester took a fourth-minute lead when former Coventry loanee Freddie Sears latched on to a pass and confidently slotted past goalkeeper Joe Murphy.
And the U's went further ahead midway through the first half when Gavin Massey finished low past Murphy, from David Wright's long pass.
Dunne said: "I've very pleased for everybody, for ourselves and the fans.
"It was a great win all round for the football club.
"It was a great start and we'd done a lot of work on this kind of play.
"Freddie took his goal exceptionally well and it was a good finish.
"Gavin has been scoring on his left foot a lot in training and he took his goal exceptionally well too.
"It was a great pass into space and a wonderful finish and we had two or three other moments where we could have killed the game off and made it a lot more comfortable than it was.
"We said at half-time that we should put the first 45 minutes to bed and to start again in the second half.
"We knew if we'd draw or win the second half we'd win the game and I thought in the end, we deserved the win."