The champions are currently 13 points behind leaders Arsenal following successive home defeats to Everton and Newcastle United respectively.
However, Carrick believes that there is enough experience at Old Trafford to see the team climb up the table in the coming months.
"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 midfielder told Sky Sports News.
"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."
United return to Premier League action today when they make the trip to Aston Villa.