Pogba scored United's first after collecting the rebound from his missed penalty before Anthony Martial added a second with a curling strike from outside the box.
It seemed the two-goal cushion would prove comforting enough until Pogba was caught dallying on the ball in midfield after which Chris Smalling's wild slide tackle gifted Gylfi Siggurdson the opportunity to claw one back from the spot.
Eventually, though, United were able to hold out for a much-needed win after a drear defeat to Juventus in the Champions League on Tuesday.
“We are playing okay,” Mourinho said after the match. “We are not as rock solid as I would like, we don't have that killer instinct I would like.
“Some teams they have three chances and score three goals. Some teams without the ball, can resist and keep a clean sheet all the time. But for us at this moment it is almost impossible to keep a clean sheet even with the phenomenal goalkeeper we have. And to score goals is really difficult for us – you can see that in this moment.”
The Manchester United manager also carefully defended Pogba's stuttered run-up, which featured a tap-dancing 26 steps, after the Frenchman's penalty was well saved Jordan Pickford only for the England goalie to be left helpless to the rebound.
“The thing I like is the desire to take it. Let me choose the words, I don’t want to be punished.
“I don’t like Mickey Mouses, fragile, afraid to go, ‘I don’t take penalties.’ I like the player that I want to take it.
“The Crystal Palace boy today he missed against Everton and today two penalties he wants to take. Paul, can he improve? I think he can. The goalkeepers know his running, they don’t move and they are waiting for his decision so he has to learn from that but for me, the most important thing is he wants to go again.”
The victory saw United climb two places in the Premier League table into eighth but they remain nine points adrift of leaders Liverpool.
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