We have to do everything that we can to achieve a good result and to stop them. Pogba's initial shot after a ridiculous approach was saved by Pickford, but the Frenchman was quick to put the rebound into the unguarded net.
Pogba broke the deadlock after 27 minutes but only after converting the rebound when his penalty was magnificently saved one-handed by Everton goalkeeper Jordan Pickford.
Pogba took a mammoth 28 steps before striking the ball.
"He took quite a long time to understand what we want, quite a long time for his brain and body to be ready for how we want him to play", Mourinho said.
"We can make mistakes on the pitch", said the Spaniard.
"But I'm not sure that the football [is what] the fans want to see. I was unfortunate. You have to go a tad early because he has so much power but unfortunately it just bounced back out".
Ultimately, Everton were left to rue a string of missed chances - most notably from the Brazilian Bernard - as United improved on a miserable run that had brought just one win from their previous seven games.
United won a penalty in the first half, which Pogba was tasked with scoring.
"I don't like Mickey Mouses, fragile, afraid, who go, "I don't take penalties".
At the moment Cesc Fabregas is yet to play in the EPL for Chelsea owing to the fact that new manager, Maurizio Sarri prefers to start Jorginho, Matto Kovacic and N'golo Kante at the midfield.
The Italian remains unbeaten since taking charge at Stamford Bridge, and Sarri was also happy with a better defensive display than in recent weeks.
"We showed character and plenty of spirit and we fought right until the end", said Pickford.
"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". I think he can.