Coventry striker Callum Wilson scored either side of half-time in a game that the hosts dominated to wipe out their 10-point deduction and climb off the bottom of the table on goal difference.
It could have been more in the end against a depleted Colchester side without Freddie Sears and Sanchez Watt, but there were no complaints from manager Dunne.
He said: "I'm not going to criticise my players.
"We were patched up, Ryan (Dickson) has had to come off again with his illness, we didn't have much in terms of quality in front of their goal.
"I know when I'm beaten and Coventry were magnificent. They were better than us, in moving the ball, passing the ball. We tried to get a passing game going in the first half and they pressured us.
"We changed it in the second half, went 4-4-2, and I've never done that as a coach, we needed to get higher up the pitch because of Coventry's dominance.
"They dominated in the first half. They were better. Clarke was getting in all the time. We had a makeshift back four, but Coventry opened us up a lot.
"But to our credit we stuck at it and it was still only 1-0 at half-time."
Coventry striker Leon Clarke hit both the crossbar and post in the opening period before Wilson converted a close-range rebound in the 37th minute.
The pattern continued after the break and Wilson added a second in the 57th minute, rounding the goalkeeper to tap in after a fantastic one-two with Leon Clarke.