Mourinho was sacked on Tuesday after two and a half years as Red Devils manager, with reports his relationship with Pogba was problematic.
Pogba was part of the United side that won the League Cup and Europa League during Mourinho’s first season.
“We won trophies with Jose and I want to thank him for that,” he said.
“He makes me improve, as a person as well, and that’s it. That’s the past, I want to thank him for that.
I’m sure that is the same for all the players and now we are looking forward to the next game.
The 25-year-old France international was speaking after United’s 5-1 victory over Cardiffin Ole Gunnar Solskjaer’s first match as interim manager.
That took them sixth in the Premier League, eight points adrift of the top four.
They finished second last season – albeit 19 points adrift of champions Manchester City – and Mourinho was sacked after a chaotic start to this campaign.
In September, he told Pogba he would not captain the team again, and a day later the pair were filmed having a tense training-ground exchange.
Pogba says he is focused on helping United “go back to the top of the league”.
“The performance of the team was great and we are happy that the first game of the manager starts like this,” he said. “It’s important now to carry on like that.
“We cannot play like this and win with five goals and then the next game lose.”