The France midfielder scored from the penalty spot to help United record a 2-1 win over Leicester City in its season-opening game, despite returning to training just four days prior to the fixture.
Pogba was given time off after helping his country lift the FIFA World Cup in Russia, although Jose Mourinho still opted to name him as captain for the Premier League opener at Old Trafford.
The 25-year-old has been linked with a move away during the transfer window, with both Barcelona and his former club Juventus reportedly interested, but he now looks set to remain with his current employer.
However, his relationship with Mourinho, who dropped the player on more than one occasion last season, including for a UEFA Champions League knockout tie against Sevilla, led to Pogba being questioned over whether he is happy at United.
"There are things I can say and there are things that I cannot say, otherwise I will get fined," he said.
"When people trust you and have confidence then you are good in your own head, it's going to be easier."
Pogba posted a message on Instagram after the game that notably did not include a reference to his club boss.
"I'll always give my best to the fans and my team-mates no matter what's going on," he wrote.