Pogba scored a penalty and a long-range effort in Thursday's Europa League group game at Old Trafford.
Pogba, a world-record 89 million pounds ($109.1 million, 100 million euros) signing from Juventus, scored a penalty and a long-range effort in Thursday's Europa League group game at Old Trafford.
The 23-year-old is yet to hit the heights since returning to United after four years in Turin, but Mourinho believes such performances will help expedite the bedding-in process.
"First of all, in some of your mouths, he goes from the worst player in the Premier League to a great player in 48 hours," Mourinho told reporters.
"I am not specifically saying it is you. I say media, especially the Einsteins. We know he is a very good player.
"We know he needs some time to show his potential. I know Italian football very well. I know teams play completely different from the Premier League.
"I am not saying we are better, but we are different: different in the intensity, the number of touches on the ball, everything is different and he needs time to adapt.
"He is a self-confident boy. He was not depressed because some people said he was a bad player. He was calm.
"It is always nice for a player to score, to score at home and especially to score such a beautiful goal."
Pogba opened the scoring in the 31st minute, netting a penalty after Juan Mata had been bundled over by Fenerbahce centre-back Simon Kjaer.
Pogba's France team-mate Anthony Martial added another penalty three minutes later before Jesse Lingard teed up Pogba to whip a first-time shot into the top-left corner from outside the box.
Lingard got on the score-sheet with another long-range effort early in the second half before United old boy Robin van Persie reduced the arrears late on, for which he received a rousing ovation.
While Pogba further endeared himself to the Old Trafford faithful, another close-season signing, Henrikh Mkhitaryan, looked on forlornly from the back row of the directors' box.
The Armenian playmaker has not played since September 10 due to a thigh problem and while he is now fit, Mourinho says he will need to knuckle down in training if he is to earn a place in the team.
"The situation is that we played with Lingard, with Mata and Martial," said Mourinho, who takes United to his former club Chelsea on Sunday.
"I am not an Einstein. I don't know a tactical system that can play with four wingers at the same time.
"He has to work more to get the intensity and fitness to play at a high level.
"To have him on the bench and give him 15 or 20 minutes like I did to Memphis (Depay), I think it is much better for him to work yesterday much harder -- and he did today in a specific session -- and wait for his chance. But he is ready very soon."
Defeat saw Fenerbahce slip from first to third place in Group A, two points below United and Feyenoord ahead of next month's return fixture against Mourinho's men.
Having finished second to Besiktas in the Turkish Super Lig last season, Fenerbahce are currently eight points off the pace in ninth place and coach Dick Advocaat is desperate for answers.
"We have to talk tomorrow about everything with the team," said the 69-year-old Dutchman.
"Maybe it's good tomorrow that they start speaking instead of me. Normally it's me, so maybe it's good when they starting speaking about everything.
"Some players last season did really well, but what I see this season is not good enough. I'd really like to know the reason."