United, who trailed in the first half when Mason Mount finished a good move involving Ben Chilwell and Timo Werner, dragged themselves level when Toni Rudiger scored a calamitous own goal, touching the ball past Édouard Mendy as his goalkeeper came out to claim the ball.
But United shot themselves in the foot again when a backpass from Kean Bryan sold Aaron Ramsdale well short. Werner raced onto the ball and touched it around Ramsdale, going down after colliding with the Blades goalkeeper.
Referee Kevin Friend didn't initially give the goal but pointed to the spot after looking at his pitchside monitor. Replays showed that Werner smashed his knee into Ramsdale's face, rather than the goalkeeper doing anything to bring the German striker down, but Wilder admitted that, on first glance, he fully expected a penalty to be given.
"It looked it from my point of view," the United boss said.
"As soon as the backpass went short and Aaron had a decision to make, everyone around us believed it was a penalty.
"I've not seen it back but I've got no real complaints about that.
"I don't think Werner gets onto the loose ball which is the disappointing thing. Aaron made a commitment to come out and these players you're playing against are cute, smart and have bags of ability. And they're showing that."