The England midfielder shone as United forged ahead early on, only for Rafael Benitez's side to roar back after the break and set up a replay for the right to reach Wembley.
"Of course we'll go there positive because it's in our nature," Carrick told MUTV. "We go there believing we can win. It's a tough place to go because they're a good team, but it's a one-off and the FA Cup can throw up some classic games. Hopefully we'll be on the right end of it next time."
Manchester City await the winners of the replay in next month's semi-final, completing a road to Wembley lined all the way by Premier League opposition, should the Reds progress past Chelsea. Nevertheless, Carrick is unperturbed by the rough route United have taken so far in this season's competition, conceding: "That's the way it is.
"If we'd beaten Chelsea then we'd have to play City in the final or the semi-final, so it's just the nature of the competition: you've got to beat
"[Stamford Bridge] is a tough place to go because they're a good team. Of course we'll go there positive because it's in our nature. We go there believing we can win."
- Michael Carrick