Fleck was dismissed for a foul on Korey Smith during the second-half of a match United controlled for long periods before being undone by Aden Flint’s 90th minute strike.
Although losing the 26-year-old for the next three games will test the depth of his squad - Paul Coutts is set to miss the rest of the season through injury - Wilder said: “I remember once, at one of my old clubs, we had a situation where all of the staff thought a player was unlucky to go.
“We had about 1000 games between us, probably more, and when you put in a request you want to make sure everyone is on the same page.
“It still got knocked back. It’s just a waste of ink.”
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“If you can’t put tackles in, the game’s gone and we don’t want that to happen,” Wilder added. “I have to be careful but even one of their lads said the same thing to us afterwards.”
Lee Johnson, the City manager, described fourth-placed United as “outstanding” despite falling behind to Jamie Paterson’s strike.
Leon Clarke’s 14th goal of the season, and 10th in six outings, deservedly dragged them level but Flint pounced at the death following David Coote’s decision to dismiss Fleck.
United, who hit the woodwork four times, remain fourth in the Championship table but without a win since beating Burton Albion three weeks ago.
“I’m not happy with the result but I can’t criticise the performance,” Wilder said.
“Those lads dominated for most of it and didn’t deserve to lose.
“They gave everything out there.”