Colchester remain three points above the relegation zone after goals from Crewe skipper Luke Murphy, from the penalty spot, and Mathias Pogba in each half, either side of George Porter's equaliser for the U's, secured the Railwaymen victory.
Dunne said: "A few things went against us, but generally I'm pleased with what I thought was a very good performance.
"We had a very difficult 20 minutes in the first half and made changes, one of which was forced and one that wasn't.
"That brought us back into the game and I thought that we deserved something from it. There was only one team that was going to win the game in the second half.
"We forced the issue and had balls flashing across the box and missed open goals.
"We've also had a couple of penalty shouts ourselves and I can't ask too much more from my players.
"On another day, we could have scored five goals, but we didn't and we were beaten by a suckerpunch. Crewe had one really good opportunity in the second half and they took it.
"That's football and it can be cruel sometimes. Sometimes it works and sometimes it doesn't, but I thought we were great after the first 20 minutes.
"There's no-one in the stadium who can question our attitude and commitment and we should have won the game."
- Sports & Recreation