The Capital One Cup finalists were forced to settle for a 2-2 draw after James Hanson was judged to have handled the ball in the area 15 minutes from time.
Substitute Jon Parkin stepped up to equalise from the spot and ensure the points were shared but Parkinson was convinced the penalty should never have been given.
"I thought we deserved three points. We got done in the end by a very contentious decision," said Parkinson. "I'm really disappointed with that, and I though they got a lot of decisions wrong.
"You get a ball smashed at a player from two yards, it's never a penalty. To drop two points in that manner is a bitter blow."
Fleetwood grabbed the lead midway through the first half. Junior Brown's effort was tipped around the post by Bradford goalkeeper Matt Duke before Alan Goodall headed home at the near post from the resulting corner.
But the visitors struck back just before the break. Nathan Pond brought down Bantams skipper Gary Jones and Nahki Wells' free-kick floated beautifully over the wall and past Scott Davies in the Fleetwood goal.
Shortly after the break Parkinson's side took the lead. Will Atkinson's long ball eluded Brown and Shaun Beeley and substitute Ryan Dickson capitalised to slot a low shot past Davies.
Parkin's penalty handed the hosts a way back into the game - his blasted effort sneaking beneath Duke.