"I want to stay here and achieve things here," Carrick told Inside United. "This is the pinnacle of the game.
"They say the easy part is getting there and the hardest part's staying there, so I've got a big challenge ahead."
However he thinks that by playing with Paul Scholes he is learning all the time.
He added: "Scholesy has been a massive influence. 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."