The triumph allowed United to wrestle back the Premier League trophy from neighbours Manchester City and Carrick is determined to keep the silverware safely locked away in the Red Devils cabinet.
"I definitely want more," said Carrick.
"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."
Since arriving at United from Tottenham in 2006, Carrick has been a part of five Premier League-winning squads as well as helping take out the League Cup and Champions League.