Mourinho's men wrapped up their pre-season tour of the United States with a 1-0 loss to Barca at the International Champions Cup, but Pogba did impress for the Premier League giants.
While United were outclassed for large periods of the match at FedEx Field, Pogba showed why the Red Devils broke the world-record transfer fee to lure him back to Old Trafford last year with his athleticism and skill against Barca.
Mourinho lauded the 24-year-old France international post-match, saying: "With Messi and Neymar, there is only one [of each]. There are not two. [Luis] Suarez, [Andres] Iniesta, [Gerard] Pique, Ronaldo, [Gareth] Bale, [Luka] Modric, Toni Kroos, there is only one of them. So they can only play for one club and not two. We cannot have them. They belong to the clubs.
"You can be working very hard tactically to improve your team, to improve your players, but some players are special and against that nature there is nothing you can do. In the real matches you try to compensate the difference in quality with a certain tactical organisation, and with that you can win.
"In football it is possible for a team to be better than the sum of the parts. But the parts are amazing. Their relationship with the ball is amazing. You can argue about the occupation of space, tactics and compact blocks, but the player's relationship with the ball is still the most important thing. Even as an opponent on the bench like I am, it is beautiful to see the guys' relationship with the ball.
"Today, one of my players, Paul Pogba, showed the level. He showed that he belongs at that level."
And as United seek to return to the summit of English football in 2017-18, Mourinho was happy to test himself against the world's best.
"If you want to compare with Real Madrid or Barcelona, it is easy to compare the level of the players and quality of the team," Mourinho said. "But we don't play in the same competition as them unless we meet in Europe, so we prefer not to compare ourselves with them.
"We prefer to compare with teams in the Premier League and we are much more adapted to that very hard competition. It has a different style, a different kind of player. In this moment the best players are in these two clubs and you have to accept that as a reality. But for us to play against both in pre-season without pressure or being worried about a result, just trying to play the best we can, was very good for us.
"Both played with their best team. Barcelona did. Only Pique was on the bench. Real Madrid, only Ronaldo and [Sergio] Ramos didn't play. So it is very, very good for us to measure against them."