The England midfielder, who signed from Tottenham for £18.6million last summer, started the majority of United's games as they won the Premier League title.
But the 25-year-old will face competition for his midfield holding role next term from his international team-mate Hargreaves.
"I want to stay here and achieve things here. This is the pinnacle of the game," Carrick told Inside United.
"They say the easy part is getting there and the hardest part's staying there, so I've got a big challenge ahead."
Carrick began his career at West Ham before moving to Spurs three years ago.
His career path has followed a progression which has taken him to what he believes is the pinnacle of the game.
"Each move was a step up really," he said. "Although when I first got in the West Ham team, we were doing really well and finished seventh that season - going down in 2003 was a big disappointment.
"But to go to Tottenham and to achieve what we did there was a big step up for the club, going so close to getting in the Champions League.
"But then to come here is another level again and there's nowhere else now!"
Carrick accepts that in order to guarantee his United future, he will have to keep improving.
He believes he has the perfect mentor in midfield partner Paul Scholes.
"Scholesy has been a massive influence," said Carrick. "Just watching him every day lets you appreciate how good he is.
"If you ask anyone in the game who's in the know, everyone says how good he is and how hard he is to play against. To have him on your team alongside you is great.
"He's just an awesome player and one that I'm watching in training and learning from, and hopefully taking things from and trying to do the same."
Carrick's tremendous range of passing was one of the main reasons Sir Alex Ferguson brought him to the club.
But the midfielder played down his own contribution and praised that of his team-mates.
He said: "I've got the easy part, they make it easy! Their movement is brilliant. It's not just where they move, it's the intelligence.
"Sometimes standing still and letting everything go on around you can create the space you need, and Giggsy's [Ryan Giggs] a prime example of that.
"He's so clever and so intelligent, you see that from some of the positions he picks up and how he does it. It's just great to have him on our team.
"But it's not just him, all of them are great. You get the ball and most of the time you've got at least two options, which is a midfielder's dream really."