"The only truth is that I made the decision that Paul will not be a second (vice) captain anymore but no fallout, no problems at all," Mourinho said after his team were knocked out of the League Cup on penalties by second-tier Derby County.
Mourinho had rested 25-year-old Pogba for Tuesday's game along with several other players.
The Portuguese declined to give a reason for his decision to take the United vice-captaincy away from the World Cup winner.
"The same person that decides Paul is not second captain anymore is exactly the same person that decides Paul was second captain -- myself.
"I am the manager, I can make these decisions. No fallout, no problems at all just one decision that I don’t have to explain," he said.
Pogba has been United's stand-in captain for three games when regular skipper Antonio Valencia has been missing.
England wing-back Ashley Young was named captain for the Derby game at Old Trafford, which United lost 8-7 in a shootout after a 2-2 draw to exit in the third round.
Pogba was critical of United's tactics in Saturday's 1-1 Premier League draw at home to Wolverhampton Wanders, saying the team should be more attack-minded.
The midfielder moved to Old Trafford in 2016 from Juventus in a $114 million transfer deal and has been linked by the media with another big-money move, to Barcelona.
In August, Pogba said that he feared he would be fined if he spoke about his feelings at United.
Mourinho said United had paid the price against Derby for failing to take their chances during spells of dominance, having taken the lead in the third minute.
"It happened that we didn’t score when we could in the first half," he said.
"We had situations to kill it, we didn’t and at halftime I repeated basically the same words I repeated in the last match that their dressing room was for sure a dressing room with belief because the result was open and they were playing quite well.
"And we need to go and kill the game which we didn’t."
(Additional reporting by Christian Radnedge; Editing by Ken Ferris and Toby Davis)
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