Bantams boss Stuart McCall was left frustrated by City's first half performance and the nature of the goals they conceded - but he still feels his side could easily have taken something from the game.
Lyle Taylor's swerving drive from outside the box twenty minutes from the end proved to be the winner for AFC Wimbledon, despite City hitting the woodwork three times.
Taylor's effort for goal appeared to swerve out of the grasp of Rouven Sattelmaier and into the corner of the goal as the German shot-stopper tried to make the save.
Before Taylor's winner, Wimbledon had originally taken the lead in just the seventh minute through Cody McDonald when the striker had raced onto a long forward pass and knocked the ball past the on-rushing Sattelmaier.
Wimbledon created chances to increase their lead during a forceful first period display, with McDonald and Taylor both going close.
Matthew Kilgallon did hit the bar for City but McCall's men weren't at their best in the opening period.
Paul Taylor's close range leveller two minutes after the break gave City the perfect start to the second half.
Even after Taylor's goal for Wimbledon, City had chances to score again and claim something from the match.
Nicky Law headed against the far post five minutes after Wimbledon's second, while the recalled Adam Thompson crashed a shot against the opposite post deep into injury time.
McCall said: "It is disappointing that we were nowhere near our very best in the first period.
"We improved a lot after the break, but you cannot expect to give the goals away that we did and still win the match.
"Having said that, we certainly didn't have any luck either.
"We've hit the crossbar in the first period, hit the inside the post through (Nicky) Lawsy in the second period, and then hit the post in the last seconds.
"We'd talked before the game about Cody McDonald's desire to get in behind, but there was that bit of indecision with us and he's nipped in.
"It was a difficuit game for us to get a foot-hold in. They were clearly boosted by the early goal.
"They were better than us in the first period. Their front two caused more problems than our front two, and their midfielders were first to too many balls and won too many second balls.
"We knew we had to play quicker in the second period, and our goal comes from getting the ball forward quickly.
"Their second goal has taken the edge off things a bit, however, and given them something to hang onto.
"The spirit the lads showed and the chances we created at the end merited more than we got out of the game.
"Both Lawsy and (Adam) Thommo's chances looked like they were going in. When that doesn't happen, you get the feeling it isn't your day.
"We have a chance to re-group now and put in a performance (vs Peterborough United) on Boxing Day."