David Moyes' men take on cross-city rivals Manchester City having endured a tough start to the Barclays Premier League season and a frustrating summer in the transfer market.
Marouane Fellaini was the only high profile arrival at Old Trafford in the transfer window and, following an opening day win over Swansea, United went on to draw with Chelsea and lose to fierce rivals Liverpool.
But they bounced back with a league win over Crystal Palace on Saturday and then followed that up with an impressive Champions League victory over Bayer Leverkusen.
City have not had it all their own way this season either after suffering a shock loss to Cardiff, and Carrick is confident United can come away from the Etihad with some reward.
"I don't think we've played that badly so far this season," the midfielder told manutd.com.
"The Swansea game was a good game, the Chelsea one was tight, but Liverpool is always a bit of a one-off game which you can't really read too much into.
"We won at the weekend, and on Tuesday we took it to another level and improved again.
"Hopefully we can do it again on Sunday. The performance will breed confidence, and we'll have to do it all again on Sunday."
Wayne Rooney was the star of the show in the 4-2 win over Leverkusen as he netted twice to bring up his milestone of 200 goals for United.
Rooney has had a tumultuous summer, with Chelsea seeing two bids turned down to acquire his services while speculation also mounted surrounding a potential move abroad.
But the 27-year-old looked more than settled on Tuesday as Moyes won his first Champions League game at Old Trafford, and Carrick was delighted to see the striker back to his best.
"It was probably Wayne's best performance that I've seen for a while," he said. "He can be untouchable when he's like that."
Rooney's strike partner Robin van Persie was also on target on Tuesday night, along with Antonio Valencia, and while neither of those two are likely to match the Liverpudlian's career goalscoring feats at Old Trafford, Carrick is delighted to see them all fully firing.
"To have lads like that in your team is brilliant," Carrick said.
"I thought Antonio was immense on Tuesday night as well and to have Wayne and Robin scoring and assisting is fantastic.
"Even if they're maybe not having the best of games they can always come up with something. I thought they played really well on Tuesday."