An unnamed source in United's dressing room said as much to the Daily Record's Duncan Castles, as the coach gave the midfielder a telling off in front of his team-mates after the match.
"You don't play," Mourinho is said to have added. "You don't respect players and supporters. And you kill the mentality of the good honest people around you."
United found themselves two goals behind after 20 minutes, as Stuart Armstrong and Cedric Soares found the net, but goals from Romelu Lukaku and Ander Herrera before half-time salvaged a point.
Mourinho wasn't the only one unhappy with Pogba's performance at St. Mary's Stadium.
Samuel Luckhurst of the Manchester Evening News and broadcaster Pilib De Brun were among those critical of the Frenchman:
Indeed, the playmaker was lackadaisical throughout, which often led to him carelessly ceding possession to Southampton:
Squawka's Muhammad Butt believes Mourinho bears responsibility for Pogba's struggles, though:
Mourinho's failure to get more from his expensively assembled squad is an ongoing concern at Old Trafford, with his side often lacking intensity or technical quality.
Their poor performances have often led to similarly poor results, as they've won just six of their 14 Premier League matches this season.
His man management has also come under scrutiny, particularly after making strongly worded comments on Luke Shaw.
However, while Mourinho's management of the team may do Pogba no favours, a player of his calibre should still be capable of producing far better than he did against Southampton.