A difficult start and two home league defeats this month have seen many right off the title hopes of David Moyes' side.
But Carrick told Sky Sports News that he is confident of making up lost ground over the Christmas period.
"Christmas period is an important time of year, wherever you are in the league," he said.
"The fact that there are so many games in such a short period you can pick up so many points up and change your situation and vice versa; you can lose some points and drop quite quickly in the league.
"Wherever we've been in the league we've always approached it the same. We've always done well to be honest and enjoyed Christmas when the games come thick and fast and we'll do the same this year.
"There's plenty of experience in the players and the manager has plenty of experience too. We'll work together and hopefully get some good results.
"The title race is wide open. There are a lot of teams up there this year, plenty of sides within touching dismtance.
"We are certainly not writing ourselves out of it just yet. We're confident we can go on a run and get right back into it. It is going to be an interesting between now and the end of the season, that's for sure."
Carrick was speaking ahead of the seventh annual Santa run at Old Trafford in aid of the Manchester United charity foundation.
"The foundation does some unbelievable work, not just locally but worldwide," he added. "The amounts of things we do when we go on pre-season tours is amazing. As players and a club we embrace it and try and do as much as we can.
"It's nice to get out in the community, whether it's schools or hospitals, and help in some way, whether it young kids or older people . If we can give back a little bit then that's great."
"It's terrific. This is the seventh year and it all helps and it's all for some great causses as well which is the most important thing.