The 21-year-old enjoyed an impressive second half of last season after Carrick took charge in January, featuring in 16 of the club's 17 matches under the former United midfielder. His performances played an important role in securing Champions League qualification, earning him a new long-term contract in April.
Although the current campaign has brought challenges for both United and Mainoo, the midfielder remains grateful for the trust and guidance he has received from Carrick and his coaching staff.
Speaking ahead of Tuesday's Champions League meeting with Roma at Old Trafford, Mainoo said: "I'm very grateful to the boss for putting the trust in me, as soon as he came in, and putting that belief in me and giving me all the advice that he has.
"He's a player who's been at this club and knows the history of this club and knows what it takes to win."
Mainoo believes Carrick's experience has helped him understand what is required to succeed at United, while also pushing him to become more demanding of himself during matches.
"I've tried to take on more responsibility in the team. I want to impose myself more in games, and they've definitely helped me to do that and given me more responsibility with taking the ball," he added.
"There's been ups and downs, but I have to continue to try and have belief in myself and impose myself on games even in these tough times."
Mainoo also spoke about his responsibility to protect Manchester United's traditions, having progressed through the club's academy from a young age.
United recently celebrated 89 years of including at least one homegrown player in every matchday squad, with the remarkable record now standing at 4,374 consecutive matches.
The midfielder believes academy graduates have an important role in passing the club's identity and values on to the next generation.
"I feel I take some responsibility in that and in spreading the word of what Manchester United is, coming up through the Academy," Mainoo said.
"I plan to send that message for hopefully as long as I can."
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