The former United midfielder will lead the team for the remainder of the campaign following Ruben Amorim's sacking last week and wants his players to produce winning football that entertains the supporters at Old Trafford.
Carrick told the Inside Carrington Podcast: "We want to win games. It goes without saying. There are different ways of doing it, different scenarios and situations in games.
"You might have to play a certain way but I think it’s working with the players and helping them get better individually which will help the team improve. It’s about being there to help support them and we’re all in it together.
"I know it comes down to results. Hopefully we can play a really exciting type of football, be positive and bring excitement. I want to be off my seat, enjoying watching the boys play and results must come from that."
Carrick won five Premier League titles during 12 years as a player at United before joining the coaching staff when he retired in 2018.
He also took charge of three games as caretaker boss following Ole Gunnar Solskjaer's sacking in 2021 before departing the club.
The former England international - who also managed Championship side Middlesbrough for nearly three years before being dismissed last summer - said of his United return: "It’s an unbelievable feeling to come back through the doors and be part of the club again. It’s been part of my life for so long and the fact that I left the club for a number of years, it’s never really left me.
"For me to be back in this position there’s two sides of it. There’s the personal side, the relationships and seeing people but I’m quickly focused on doing the job. It’s a big responsibility, a massive pleasure and a privilege to be here.
"We want to do a good job and this place deserves that."