The Red Devils could have taken all three points at Anfield if Alisson had not denied Pogba with less than ten minutes remaining.
Pogba slammed his hand against the ground after the miss, and the Metro claims the Frenchman was still furious in the dressing room once the match ended.
The World Cup winner took the blame for the draw in front of his teammates.
After being in and out of the team at the start of the season, Pogba has played every minute of United's last four matches.
They will be hoping to return to winning ways when they face Fulham at Craven Cottage on Wednesday.