Pogba has received widespread criticism this season for his performances in a United shirt, often having little impact and failing to exhibit his obvious talent.
He was particularly ineffective during the first half at the Etihad, as Jose Mourinho's men were left trailing 2-0 at the break and facing the prospect of seeing City clinch the Premier League title.
But Pogba produced a fine second-half display which included two excellent goals to inspire a turnaround and he later said a conversation with Carrick – who is set to join Mourinho's coaching staff at the end of the season – played a major part.
"I just kept it simple and said 'this is what you are' and 'this is what you're good at'," Carrick told Sky Sports about his chat with Pogba.
"But listen, he scored two goals, so it's not down to me.
"I'm glad I did [have an impact] because it shows little things do register with players."
Carrick's long and illustrious career will draw to a close when the Premier League season concludes and his move into coaching is something he did not expect to do a few years ago.
"Three or four years ago I probably wouldn't have thought I'd go down that route," he said. "It wasn't until I started my coaching badges that I found that I enjoyed it.
"Eventually, I think I would like to be a manager. It looks easier than it obviously is, but of course it's not easy.
"There is an element that keeps nagging away at me in games where I think what I would do there and what would I change."