The deadlock was broken in first-half stoppage-time when Billy Clifford's fine 25-yard strike flew into the top corner.
Colchester doubled their lead just after the hour-mark when Freddie Sears drilled home from close range after Bradley Garmston had done superbly to race to the byline and pick him out.
Dunne said: "To a man, we were excellent. Based on what happened against Tranmere, it was probably one of the best performances we've had.
"We had a great reaction from the players and we need to show more of that now to get out of where we are, because that's the kind of performance it's going to take.
"It's not going to work all the time, but when it does it looks good and it was needed.
"There were a lot of good performances and I just felt that by hook or by crook, we were going to keep a clean sheet.
"We threw bodies in front of things, we headed and we tackled and that's what it takes when you are where we are in the league.
"We also had the quality when we needed it, but the main focus was to get the result and my players conducted themselves in a fantastic way."