The Geordie scored in last night's win over Northampton to set up a tie with Manchester City.
"I'm desperate to win trophies," he told MUTV. "That's why we're here and it's why I'm still playing. We've said from day one of this season that we want to be challenging at the end of it."
The win at Sixfields Stadium brought United out of a spell of three consecutive losses and Carrick wants the positive reaction to continue in the weekend's Premier League clash with champions Leicester City.
"We had a setback last week," admitted Carrick, "but it's not going to finish off our season. It's about how we react to it. We had a good start with the first three or four games of the season and we want to get back to winning. We did that tonight.
"It's a big game on Saturday and we want to get our season back on the right road. Come the end of the season we want to be challenging."