The Red Devils secured their 20th top-flight title with a 3-0 win over Aston Villa at Old Trafford on Monday, with four games still to play this season.
"I definitely want more," Carrick told Sky Sports News. "The season is not over yet, we haven't even got the trophy, but, when we come back next year, we will be as hungry as ever.
"I said before I came here that, if I won a league, that would have meant everything to me. Strange as it seemed, as soon as I won that first title, it left me hungry for more.
"The satisfaction of winning is such a good feeling you want it again and again, and you get hungrier to win it again."
Carrick has been at United seven years, since joining the club in 2006 from Tottenham Hotspur.