The former Red Devils star earned the permanent role after an impressive interim spell, guiding United to a third-placed Premier League finish and Champions League qualification.
However, Carragher remains unconvinced about his credentials at one of Europe’s biggest clubs.
Writing in his Daily Telegraph column, the former Liverpool defender argued that Carrick would not have been considered for the job by another elite European club.
"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 wrote.
Carrick will face his sternest test yet when Manchester United host rivals Manchester City at Old Trafford this weekend.