Louis van Gaal's side maintained their position in the top four with an emphatic 3-0 defeat of Hull City at Old Trafford on Saturday.
That was United's third straight victory and the Dutch manager hailed the performance as their most convincing of the season so far.
Carrick echoed those thoughts and feels United are beginning to settle into a rhythm, even though Angel di Maria looks set to be missing after limping off early against Hull.
"It was a good performance and a good win," Carrick told MUTV. "We controlled the game from the start and played some really good football. Hopefully there will be more of the same on Tuesday."
"Our downfall this season is that we've had to change the team too much and we haven't had a consistent run with this squad.
"Hopefully that will change now and it's nice to have a game so quick so we can keep that momentum going.
"It was a good performance and win against Hull but it's behind us now and our focus is on Tuesday."
United fans will have been particularly pleased to see Robin van Persie silence his critics with a superb goal after he came under fire for a lacklustre showing versus former club Arsenal.
"It was some strike," added Carrick. "It was only really half a chance, but he's controlled it and smashed it into the top corner.
"It's great when the boys up front are creating chances and scoring goals. If we can do what we did on Saturday on a more regular basis, we'll be a real threat."
Stoke must try to recover from suffering back-to-back defeats against Burnley and Liverpool since returning from the international break.
Mark Hughes will at least have taken some comfort from the impressive performance of Bojan Krkic at Anfield, with the Spaniard unlucky not to score with one particular effort which came crashing back off the post.
"He was the best player on the pitch, there was no doubt about that," said Hughes.
"He's up to speed now and getting to grips with everything. You can see that he's stronger than he was at the beginning of the season.
"He's always looking to be positive with his play and technically he can receive the ball in tight areas, which is important for us. He's getting better with every game now."
Steve Sidwell (knee) and his replacement Glenn Whelan (calf) were both forced off with injuries at Anfield and appear unlikely to feature for Stoke against United.
However, Phil Bardsley will hope to return at right-back after missing the Liverpool game due to a sickness bug.
