Blades midfielder Barry Robson opened the scoring with a fourth-minute penalty after being fouled by Colchester defender Josh Thompson.
Kevin McDonald added a second with a low, long-range effort in the 73rd minute and Dave Kitson completed the scoring in stoppage time after Diego De Girolamo's shot had been parried by Colchester goalkeeper Sam Walker.
Dunne, satisfied with his side's performance, if not the scoreline, said: "It's a disappointing result, but I thought overall that we had a really good go at them and posed a threat at times.
"We were confident going into the game and the whole thing changes straight away when we conceded a penalty. I understand why he gave it, but I think he (Josh Thompson) made a genuine attempt to win the ball.
"We responded well and created some chances, but there was never really an end product. Right up until the second goal, I thought we were right in the game.
"I thought there were some good performances from some of our players. I thought Bradley (Garmston), who was making his debut at left-back, was excellent.
"I was very disappointed with how the late goal came around. It was the responsibility of the players to track their runners.
"It hurt more to lose by three goals because, don't forget, goal-difference is important as well. We need to stay focused because we're still down there and we need to bounce back.
"We've got some good young players and they're learning the hard way. I'm really pleased with the effort being shown by the players and they're going to have to keep working hard."