United's 1-0 victory over Arsenal at Old Trafford on Sunday means David Moyes' men head into the international break just five points adrift of the Gunners, who remain at the top of the Premier League.
It is an impressive recovery from the reigning champions, who dropped into the bottom half of the table in the middle of September after losing at home to West Brom.
But even after suffering that third defeat in six games which yielded just seven points, Carrick was never tempted to hit the panic button, with United now on a nine-match unbeaten run in all competitions.
"After a shocking start we are not in a bad position," said Carrick.
"We never really got too despondent. We were frustrated with our performances and results but you have to stay patient and trust yourself.
"We knew there was a long way to go and there still is."
United defender Phil Jones has suggested some people have been hoping for United to fail, having become jealous of their immense success under Sir Alex Ferguson.
However, Carrick does not view it in quite such graphic terms and he feels some of the criticism for their sluggish start was deserved.
"You can take it as a compliment because of what we have done over the years," he said.
"When we are not at the top, because of our recent run in the league people are asking questions and criticising.
"In some ways it is fair. In others we take it with a pinch of salt. We have to deal with it from within.
"A few weeks ago we probably didn't think we would be in this position as quickly. Now we are not in bad shape, although it is still very early."
After early season failures to beat Chelsea, Liverpool or Manchester City, Sunday's result also quashes the claim that Moyes may struggle against United's major rivals.
And that should ease the nerves of the fans who remain uncertain about Moyes being the right man to take on the unenviable challenge of replacing Ferguson.
But Carrick always felt there would be some period of transition required after such a seismic change.
"Obviously with the new manager and new staff coming together and gelling, (defeating Arsenal) helps the feeling within the club," he said.
"It is easy to jump on the bandwagon when we have lost a game or two and people are saying it is all wrong.
"We knew that wasn't the case but this result has put us in a better position and now there is a bit of stability."