Mourinho was sacked on Tuesday after two and a half years at Old Trafford, with speculation rife that his relationship with Pogba was unpleasant.
“We won trophies with Jose and I want to thank him for that,” Pogba 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.”
Pogba was a constant part of the French team that won the FIFA World Cup in July, but often found himself on the sidelines at Manchester United.
The 25-year-old seemed to have a see-saw relationship with the Portuguese tactician, with videos at times emerging online of their different encounters.
Mourinho’s sacking came following a 3-1 loss to table-toppers Liverpool, with fears mounting over the possibility of United not going to finish the season in the top four.
Mourinho’s replacement Ole Gunnar Solskjær got off to a winning start on Saturday, crushing Cardiff City 5-1.
Followng that emphatic win, Pogba said he is focused on helping his side “go back to the top of the league.”
“We cannot play like this and win with five goals and then the next game lose.”
United are currently ranked sixth, eight points behind fifth placed Arsenal and 19 points behind League leaders Liverpool.