United find themselves in the unfamiliar position of underdogs going into Sunday's third round tie, but Carrick is confident that his teammates are good enough to challenge in both the cup and the league.
"People can say what they like and fancy who they want," said the 30-year-old. "We know what we can do. We know the players we have got in the dressing room.
"We just want to be back to top form and winning the game, regardless of the situation in the League, really.
"Nothing has been handed out. No trophies have been awarded. We just want to be in there and there at the end. The cup is different. We want to produce that now."
The last time the two Manchester clubs met, City came out on top with an emphatic 6-1 win.