The Red Devils went behind after 27 minutes into the game when Steven Bergwijn blasted a shot past David De Gea.
Manchester United got the equalizer on the 81st minute mark from the penalty spot through Bruno Fernandes after Paul Pogba, who was introduced midway through the game, was tripped inside the hosts’ penalty area.
The visitors were awarded a second spot-kick during the dying embers of the game, but VAR overturned referee John Moss’ adjudication after the collision between Eric Dier and Fernandes was deemed to not be a foul.
In an interview with BBC Radio 5 live after United’s stalemate against Jose Mourinho’s men, Solskjaer lauded his side for playing well but was gutted with the result, insisting the Manchester-based club should have won the game.
"Good performance, disappointed with the one point. I think we deserved more. I think the performance deserved three points,” the former Cardiff City head coach said.
"We started off slow, dominated possession yes but too slow then we conceded a sloppy goal - disappointed with that one.”
“We had a bad five minutes after that one but after that I think it was only a matter of time before we got the goal.
"Hugo Lloris made a fantastic save and we should have had more goals."
The result leaves Manchester United two points ahead of Sheffield United in fifth and two points behind fourth-placed Chelsea.
