Paul McCallum, on loan from West Ham, bagged the winner in the 58th minute and the Dons held out comfortably for the win after Dale were reduced to 10 men with Joe Rafferty's dismissal for a second bookable offence.
The home side hit the crossbar with a Bobby Grant free-kick early on and tested Dons stopper Neil Sullivan courtesy of Andrew Tutte's shot midway through the first half, but little materialised after the break.
"I'm not happy after that and I'm bitterly disappointed for the fans, because they deserved better than that," Coleman said.
"The first half was a bit of a non-event. We controlled it but we didn't really hurt them. We had a shot at the bar and one straight at their `keeper, but that was about it.
"We spoke to them again at half-time about how we should play but they (AFC Wimbledon) came out, put us under a little bit of pressure and we haven't cleared our lines on three or four occasions and then let a stupid goal in.
"We had a man sent off for a silly challenge then huffed and puffed late on but we never had anywhere near like the number of shots on target that we should.
"I can't get my head around why we can put in 31 shots at target against Exeter and, no disrespect to Wimbledon, but against a team which has conceded 46 goals and went into the game bottom of the league, we have only tested their goalkeeper once. That doesn't add up."