Substitute Marouane Fellaini headed Manchester United into a deserved first-half lead and compatriot Romelu Lukaku followed suit early in the second period with his first goal in the Champions League group stage.
Marcus Rashford came off the bench to net his first goal in the competition and wrap up a 3-0 win against Basle on a night when Pogba's hamstring complaint took the gloss off the Group A victory.
An evening that started with him leading United out as captain for the first time was brought to an halt inside 19 minutes, with the 24-year-old reportedly seen leaving Old Trafford on crutches.
"I don't know (what the severity is)," Mourinho told MUTV. "I just know from experience it's a muscular injury. In my experience, muscular injury stops you from playing for a few weeks, I think.
"It looks for me too (like a hamstring injury) but I haven't spoken yet to the medical department. Squads are for this, squads are for injuries, squads are for suspensions. We don't cry with injuries.
"So if no Paul for Sunday, we have (Ander) Herrera, we have (Michael) Carrick, we have Fellaini and we have (Nemanja) Matic."