The world’s most expensive player, who returned to Old Trafford from Juventus in the summer, opened the scoring with a penalty before claiming his second with a long-range strike after Anthony Martial had doubled the lead with another spot-kick.
Jesse Lingard added the fourth early in the second half, prior to a consolation from former United forward Robin van Persie.
Speaking about Pogba, Mourinho told BT Sport:
“Two days ago, he was the worst player of the Premier League and 48 hours later he’s phenomenal.
“He needs time. I was in Italy, I know Italian football, I know the characteristics, I know the pace, I know the intensity and to be in Italy for four or five years and then come back to the Premier League I was not expecting (him to adjust) in a click of fingers.
“He needs time, even the top players sometimes they need time but I’m happy with the performance today because he gave us what we need.”
Mourinho also insisted Pogba was his side’s designated penalty taker, with captain Wayne Rooney having taken them in the past.
“The first penalty taker was Paul, we made that decision and then probably he didn’t want to repeat because it’s a second penalty a couple of minutes later,” Mourinho added.
“And then probably because Martial was the one that had the previous action and Martial also is a good penalty taker, they made that decision, it’s not a problem for me.
“I always give the indication of the one who has the responsibility to take but with the freedom for the other guys to make a decision on the pitch.”
The win puts United level on six points with Feyenoord at the top of Group A after Mourinho’s men were beaten by the Dutch side in the opening round of matches.
“After a defeat in the first match, it is very important for us to make nine points at home and try (for) a few more in the matches away so a very important victory for us,” Mourinho continued.
“I think they came with a good defensive plan and they stopped us for the first period of the game but then they we had the first two goals, two clear penalties which opened the door for quality.
“I think we played well for periods but then with the fourth goal I think we stopped which is natural and they tried to have a reaction, which they did.
“I’m never happy to concede a goal, especially if the goal is not a perfect one. The important thing is we have six points and two victories at home.”