After a mixed start, the Red Devils clash with rivals Manchester City on Sunday afternoon in what should be a thrilling derby between two sides who won their midweek clashes against FC Porto and Sabah.
Carrick was appointed as caretaker back in January, following the sacking of Ruben Amorim and quickly took the side back to the Champions League in what was an incredible achievement.
Despite his success, Carragher told The Telegraph that Carrick still has his interim label which will be almost impossible to shake off.
"To most, it feels like Carrick remains an interim solution in all but name, entrusted with the keys to Old Trafford until a super coach can move in during the summer of 2027. Carrick will not see it that way, of course, but there are certain perceptions which will be tough to shake off.
"He is viewed beyond Old Trafford in the same way as Ole Gunnar Solskjaer when he was handed the job full time. Their credential for getting the caretaker role in the first place was their status as club greats. Once they performed well it was a sensible and emotional choice to give them the chance to make it work long term.
"That cannot change the fact that based on their coaching CVs alone, they would never have been approached by another elite club in England or Europe, nor would others have had any sentimental attachment to consider when determining the merits of offering a permanent deal."
Despite the harsh words from Carragher, Carrick is aiming to become the first United manager in 113 years to win both of their opening Manchester derbies in the league.
A win would not shake off the interim label but would put Carrick on his way to raising his reputation, something that could be altered if he brings silverware back to the side.