The Premier League record points total of 95 is still within reach, but Carrick believes the champions have a duty to perform in the remaining games anyway.
Third-placed Arsenal will certainly be up for it as they are aiming to secure a Champions League place in a close battle with Chelsea and Tottenham that looks set to go to the wire.
Carrick told ManUtd.com: "We’ll approach it the same as always because our pride dictates that we want to win the game.
"We’ve won the league but we won’t go there and relax; we want to put on a good performance and try to play as if the title depended on it – that’s how we’ll approach it.
"Of course we’re in a position where we can play with a bit of freedom but we still want to get a result, so we won’t be taking anything lightly.
"We don’t want to take our foot off the gas; we want to carry on until the end of the season. It’s only fair to us and the other teams that we do as much as we can."
Sir Alex has outlined his desire to involve the fringe players in his squad in the final few games and Carrick can appreciate why.
"The big thing about this season is that everyone has played a part; everyone has contributed to us winning the league," the in-form midfielder added.