The U's were the better side for long periods of the game but came away empty-handed after David Cotterill scored a stunning match-winner six minutes from time.
"I thought we were magnificent and didn't deserve to lose," said Dunne. "We executed a game plan absolutely spot on and it's one of the those games as a manager when you're left scratching your head.
"We have to recognise we lost the game at the end of the day and we are all devastated about that, but the players should be proud of themselves. I couldn't have asked for more from them and if they continue to play like that we are going to get out of the situation we are in."
Colchester had the ball in the net on the stroke of half-time when Josh Thompson headed home but the effort was disallowed for pushing.
Dunne added: "I thought it was a perfectly good goal, but that's the way it goes when you are struggling near the bottom.
"It's hard to take, but we just have to keep believing in ourselves because we will win more than we lose if we play like that.
"It's tough losing again after a performance like that but I'm really proud of my players. It took a wonderful goal to beat us, but really that's no consolation at all."
Cotterill capped a mazy run with a curling shot into the roof of the net for his 10th goal of the season.
- Sports & Recreation
- David Cotterill