"We wanted the win because it was really important and now we are top of the group and are looking forward to the next game," said the £89m midfielder.
Wayne Rooney was back in the side but Pogba wouldn't let the England striker slot home a penalty after Simon Kjaer clumsily bundled into Juan Mata.
"I told Wayne (Rooney) I wanted to take the penalty and he let me," he added.
"I am very happy to score that penalty and from a player like him to let me it is big respect so I am very glad.
"I feel comfortable with all of the team. It is just at the start of the season and there is still a long way to go and we want to go up and do our best and be top of the league."
After very little of note in the opening half an hour, Pogba and Anthony Martial netted penalties within three minutes of each other before the former scored a fine third in first-half injury time.
Jesse Lingard added a fourth just after half-time and the United fans were on their feet again for Fenerbahce's consolation goal, scored late on by their popular former striker Robin van Persie.
Boss Jose Mourinho knew his side needed to win all of their home games in the Europa League and he was very happy with "two clear penalties."
"It is three points and that is what we needed," said Mourinho.
"We knew after the first defeat it was important to get nine points at home and a few more away so it was a very important victory for us.
"It was good. They came with a good defensive plan and stopped us for the first period but then after the first two goals, both clear penalties, it opened the door for quality.
"With the fourth goal we stopped and they tried to have a reaction which they did.
"I am never happy to concede a goal.
"We lacked a bit of concentration but that is the nature of the players and lots of changes, it is acceptable."
The impressive United performance was watched by former England boss Sam Allardyce who sat beside Sir Alex Ferguson at Old Trafford.
Mourinho also hailed the class of Pogba, who dazzled at the Theatre of Dreams.
"Two days ago he was the worst player in the Premier League and 48 hours later he's phenomenal," said Mourinho, referring to criticism aimed at Pogba after his performance in Monday's goalless draw with Liverpool.
"He needs time. I'm happy with his performance because he gave us what we need."
United are level with Feyenoord on six points, two clear of Fenerbahce at the halfway point in Group A with a trip to the Turkish side in a fortnight next.
Tougher tests will come - not least the visit to Chelsea in the league on Sunday - but Pogba appears to be in the mood again.
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