The Red Devils have endured a disappointing first season under David Moyes and find themselves down in seventh with six games to go.
However, Carrick claims that there have been difficult seasons in the past and the club has always come back stronger.
"An awful lot can change from season to season," he told reporters. "So we are looking ahead thinking we can challenge again.
"We have the potential to come back stronger next time - that is something we have always believed in as long as I have been here.
"There are certain times here through the years when we have had two bad results on the spin and the roof caves in and everything is wrong. This season it has been over a longer period but, hopefully, next time around we can get back to winning more often."
Manchester United travel to Newcastle United tomorrow.