McCall's men deservedly led at the break thanks to Jordy Hiwula's eleventh goal of the season but a close range finish from former Bantam Devante Cole midway through the second period got the hosts back in it.
Fleetwood then completed their unlikely comeback nine minutes from the end when a cross from Conor McLaughlin deflected in off Stephen Darby and Josh Cullen following a quickly-taken corner.
McCall was understandably downbeat after his side's second half reversal but he knows his players will be ready to bounce back at the weekend when they host Bolton Wanderers.
The City chief said: "We've scored first, something we've not been able to do in a while, but we've once again not be able to pick up a clean sheet.
"We were looking comfortable against a good side and limiting them to very little.
"One of the first real chances they do get, however, we allow them to get in down the side too easily and we don't defend our near post well enough.
"With the winning goal, we've just switched off. It is unprofessional from us.
"We are unfortunate with the way it has come off Josh and gone in but we've switched off from the corner and it has cost us.
"I think the main turning point came in the second half when young Gilly (Alex Gilliead), who was terrific for us, fired over with the goal in front of him. That would have made it 2-0 to us at that point.
"You could say that would have been game over then.
"This defeat is naturally a hard one for us to take - giving poor goals away has ultimately cost us.
"We've come here away from home, won the midfield battle, worked well to get through their three centre halves for the goal, but it is the result that obviously means everything at the end of the day.
"We can say that this part of the performance was good and that part was good but we can't get away from the disappointment that we've lost a game we shouldn't have.
"This is yet another game this season that we should have got more out of.
"It is becoming too common, and it must be hard for the fans and players to take at the moment because our performance tonight (Tuesday) didn't merit us losing.
"We mustn't feel sorry for ourselves though, we have fourteen games to go and a big match (vs Bolton Wanderers) on Saturday to look forward to.
"We will come out fighting at the weekend and give it a really good go."