The 31-year-old has won five Premier League winner's medals at Old Trafford since leaving Tottenham in 2006 but insists that he has no intention to rest on his laurels.
"I said when I signed that one trophy, or winning the league once, would mean everything to me," Carrick told the Daily Mirror, "but you win it once and you want a second. It just keeps going and snowballing after that.
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United secured the title with four games remaining, a stark contrast to losing out to Manchester City in the final minute of the previous season.
Sir Alex Ferguson and his side will receive the trophy following their final home game against Swansea City on May 12 and Carrick is relishing the prospect.
"Winning it this season was special," the midfielder added, "and it will be a special day when we pick up the trophy.
"It's special enough just to win each one but when it has been taken away from you, to get it back in the fashion we have after the way last season ended is even more special.
"For us to bounce back like we have shows the character of the squad, the character of the boys. There's a lot of satisfaction at the achievement."