Pogba, 24, was in impressive form as United cruised to a 2-0 win over Burnley on Sunday (23 April) but the afternoon appeared to end on a sour note for the France international.
Moments after seeing his shot veer just wide of Tom Heaton's goal, Pogba fell to the floor before he was replaced in stoppage time by Michael Carrick.
Along with Eric Bailly, who also looked to be struggling at the end of the game at Turf Moor, Pogba played all 120 minutes of last Thursday's Europa League quarter-final tie against Anderlecht which went to extra-time.
Mourinho singled out Bailly and Pogba for particularly high praise after the win that moved his side to within a point of fourth-placed Manchester City but admitted Pogba was feeling "dead" after an exhausting week.
"I don't know," Mourinho said post-match, the Manchester Evening News reported. "Dead he is for sure. If he is injured or if it just the super accumulation of fatigue in the muscles, I don't know.
"But as I was saying, if he cannot play Thursday he cannot play Thursday. We play another one and we don't cry, like we did today."
Mourinho made eight changes to the side that edged past Anderlecht with Anthony Martial and Wayne Rooney both scoring on their returns to the starting XI. With Zlatan Ibrahimovic and Marcos Rojo joining Chris Smalling, Phil Jones and Juan Mata on the injury list, the United boss is calling on every member of his squad to deliver when called upon.
"This moment is a moment for everybody to give everything they can," he told Sky Sports.
"Of course not playing for such a long time and being injured for a few weeks, I don't believe he is at the top of his form.
"I don't believe he has 90 minutes but he has the mentality and the desire to help us. That for me is really important."