Barcelona dealt United their first defeat of their pre-season campaign, with Neymar's first-half goal enough to see off Mourinho's side - which featured eight changes from the victory over Real Madrid.
Pogba returned to the starting line up, along with £90m summer signing Romelu Lukaku, and the midfielder's performance convinced his United boss he deserves to be placed in the category of irreplaceable players at Barcelona and Real Madrid.
"(Lionel) Messi and Neymar, there is only one; there is not two," said Mourinho after the game. "(Luis) Suarez, (Andres) Iniesta, (Gerard) Pique, (Cristiano) Ronaldo, (Gareth) Bale, (Luka) Modric, Toni Kroos; there is only one so they can only play for one club, not for two clubs.
"We can't have them, they belong to the clubs. But I have to say that Paul Pogba showed the level... he showed he belongs to that level."
Pogba, Anthony Martial and Andreas Pereira had their chances on goal to equalise for United in the second half at the FedexField but failed to test Barcelona stopper Jasper Cillessen as they
Mourinho insisted it was important for United to finally lose in their last game of their US tour though.
"It's very important to lose a match in pre-season," Mourinho said.
"I think it would be very bad for us to leave the U.S. without a defeat, playing against teams like Real Madrid, Barcelona, Manchester City, it would be very bad to go home with just victories.
"I think in the game we did some very good things and we did bad things. The very good things are to keep and the bad things are to improve."