United captain Wayne Rooney scored the winner late in the second half as the 30-year-old registered the away side’s only shot on target on Merseyside.
David De Gea had to make a flurry of saves to deny Emre Can twice and Roberto Firmino, but Liverpool couldn’t beat the United goalkeeper despite the introduction of Christian Benteke.
Former United shot stopper Schmeichel wasn’t impressed with the manner of the Red Devils’s victory despite a vital win against their bitter rivals on Sunday afternoon.
“How Manchester United won that, I do know know,” Schmeichel told Sky Sports.
“It’s the way football is being played at the moment. Not a lot of things are happening in the games. It was a set-piece and the other teams switches off slightly, and Man Utd took advantage of that.
“It was three unexpected points. United didn’t play very well at all.”
Rooney’s winner was his sixth goal in 24 appearances for Everton and United against Liverpool since his first strike at Anfield in 2005.
The England striker is seven goals behind Sir Bobby Charlton’s record of 249 following his winner at Anfield.
Louis van Gaal’s side are in fifth place and two points behind Tottenham Hotspur.
Get 8/1 enhanced odds on Tottenham to win or 11/1 enhanced odds on Liverpool to win at White Hart Lane on Saturday afternoon. Click here to sign up now. T&Cs apply.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news