The Red Devils passed up the chance to leapfrog Manchester City back into top spot as they succumbed to Chris Wilder’s side, who had won only one game in the Premier League all season.
Kean Bryan headed home the visitors’ first goal after a cross from John Fleck inside the opening 23 minutes. Sheffield then soaked every pressure and took the lead into halftime.
Solskjaer’s men got their equalizer midway through the game when former Sheffield United defender Harry Maguire scored his first goal at Old Trafford.
Manchester United’s hopes of completing another comeback in the Premier League vanished into thin air when substitute Oliver Burke struck the winner through a big deflection off Axel Tuanzebe on the 74th minute mark.
"Disappointed, we couldn't get to the heights of the last few months' football we played. Very disappointing, we couldn't find a solution to their very compact block and good defence,” Solskjaer said after the game.
"Two wrong decisions, that's how it is, it's that kind of season, inconsistent and the referee missed those two.
"That little spark, that edge, we didn't have that extra creativity, imagination, the X factor we've had in recent weeks. We looked at it, I agree it is not good enough, so go again.
"We conceded a poor goal, lost the ball cheaply up the pitch, didn't get back in and tackle, didn't clear our lines and didn't get out to the ball quick enough and we were punished.
"There is no time to feel sorry for yourself because Saturday you go again, we have Arsenal, we have to forget this, learn from it and move on."
