The Red Devils are unlikely to finish in the top four and are currently 11 points adrift of the final Champions League spot.
In contrast, City are fighting for the Premier League title, with Liverpool and Chelsea currently standing in their way.
"I don't think [the derby] matters," ESPN quotes Carrick as saying. "It's just another game for us - a big game, but it's not going to repair any of the damage that's been done in recent months by us losing games.
"Beating City would help us in terms of keeping our run going. We understand the fans and the result they want and for us as players it's exactly the same, but we're still not getting carried away because of the season we've had."
United are currently seventh in their domestic campaign, but remain in contention for the Champions League as they prepare to face Bayern Munich in the quarter-finals next month.