The Red Devils held the aces as they went two goals up before the break, thanks to Edinson Cavani’s 24th minute opener and an audacious execution from Bruno Fernandes on 45 minutes.
Manchester United’s lapse in defensive prowess after the break allowed the Toffees to claw their way back into the game, courtesy of goals from Abdoulaye Doucoure and James Rodriguez inside 49 and 52 minutes respectively.
However, Solskjaer’s men re-established their lead with a flicked header from Scott McTominay on the 70th minute mark and that seemed to have settled matters at Old Trafford, but England striker Dominic Calvert-Lewin’s late equalizer made sure the match ended in a draw.
"We deserved to win the game but that is football for you, you have to take your chances and cannot concede with every shot,” Solskjaer said after the game.
"First half I did not feel we played particularly well but scored two fantastic goals, you go in at the break 2-0 up feeling we have not hit where we could do. After 2-2 we played really well then the last kick of the ball kicks us in the teeth and go home disappointed.
"Paul could not carry on, a muscle injury and will have a scan in the morning to see how he recovers.
"We have to focus on improving as a team, we are scoring more goals, creating chances and you felt you dominated the game and should have won it. The fans can see we are team that is trying to go for it, even at 3-2 up we wanted to get the fourth."