Blades escaped with a point at Bramall Lane in a goalless draw against winless Birmingham, but it was Garry Monk’s side who came closest to taking all three points.
Substitute Omar Bogle fired over from two yards out, Connor Mahoney spurned a one-on-one with Dean Henderson and the Blues hit the post twice as they created the better openings at Bramall Lane.
But Blades boss Wilder, marking his 100th game in charge at Bramall Lane, revealed that the swift turnaround was behind his decision to make five changes from the side that lost 1-0 to Bristol City on Saturday.
“Not a free-flowing performance,” he said. “I felt we had to because of the schedule.
“I could have changed it for Saturday but I went for tonight so maybe I’ll take a little bit of the blame. There’s an EFL meeting tomorrow so I think our club will raise the issue. I don’t know if we’ll get an answer but we’ll put a letter in.”
Monk believes his side will soon start turning draws into wins after picking up a point for the sixth time this season.
“We knew it was going to be a really tough game for us,” he said. “I thought it was a very good away performance - first half we were very solid, then second half I thought we really stepped it up and were the most dangerous team on the pitch.
“If anyone was going to win that game it was us. Everyone wants to say it’s a winless run which we understand - anyone that’s seen us this season we’ve deserved a lot more than what we’ve got.