Having moved swiftly to quell talk of an imminent Wayne Rooney departure from Old Trafford, United must now set their sights on those "noisy neighbours".
Rare indeed are the days when United are spoken about as a team who might inflict a shock rather than suffer one.
But that is exactly what will happen on Sunday if Sir Alex Ferguson's men reach the FA Cup fourth round by winning at the Etihad Stadium.
It would be seen as further proof that the old guard is changing, following on from last season's FA Cup semi-final win for the Blues, October's staggering 6-1 win at Old Trafford and a Barclays Premier League table that has Roberto Mancini's men three points clear at the top.
However, Carrick is preaching caution.
As the veteran of four successful championship campaigns and a Champions League triumph in 2008, the 30-year-old knows what it takes to win silverware.
And, despite recent mishaps, the former Tottenham star is adamant United still have what it takes.
"People can say what they like and fancy who they want," said Carrick, over odds that have a United win as the least likely of the three potential results.
"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 hang in there and be there at the end.
"The cup is different. We need to produce that now.
"It would be nice to knock them out. More importantly it would be nice to progress."
That clarity of thought might be needed after a chaotic build-up.
Successive defeats to Blackburn and Newcastle were bad enough.
But last night came the apparent bombshell of a schism between Rooney and Ferguson that was so bad, it might lead to the striker's exit during the present transfer window.
Reaction, from club and player, was swift.
United labelled the speculation "nonsense", whilst Rooney was unequivocal in a Twitter posting that followed immediately after the statement was released.
Rooney wrote: "My future is with Manchester United and the club and I are totally committed.
"The manager and I have no issues and anyone who says different doesn't know what they are talking about."
Still, the episode hardly helps preparations to face opponents who have won every Premier League game they have played on home soil this term, their latest victory coming on Tuesday, when they cruised past Liverpool.
In fact, the only time they failed to win at home during 2011 was when they drew with Fulham, a traditionally obdurate opponent, in February.
"You have to be impressed with Manchester City," said Carrick.
"They have some great attacking threats and can hit you at any time and cause problems.
"At the same time, they are a good unit and they are solid and difficult to break down. That is the makings of a good team.
"They have had a little blip, as we did, over Christmas. But they got the big win against Liverpool and they will be looking forward to the game as much as us."
It all adds up to a mouthwatering tie, which threatens to take United's skirmishes with City beyond all the other rivalries that have built up over the years.
Carrick is not complaining though.
He relishes the intensity of such occasions and the more he is involved in, the better he likes it.
"The fact they are up there adds to the intensity of this local derby," he said, "It has gone to another level from when I came.
"But that is great. You want to be playing in the real pressure games, when the whole lot matters.
"That is when you really test yourselves. In the past, we have been really good at finding a way to win these games. We will be focussing on doing that on Sunday."