Sunday's loss to the Reds was seemingly the final in the coffin for Mourinho, who leaves after two-and-a-half-years in charge at Old Trafford.
But Carragher, who insists United have a 'failing squad, not a poor one, ' claims both managers and players must take their share of the blame for United's demise.
"It's about making sure the next manager is the right manager", he said.
Then there was United's pragmatic and often-ponderous style of play under Mourinho that always seemed at odds with the team's preference down the years for free-flowing, attacking play.
The club said the new manager will understand the philosophy of the club, including its attacking traditions.
"I am really, really happy with the players that I had on the pitch, with their attitude, with their effort".
They could have been pitted against any of Bayern, Barcelona, Real Madrid, Juventus, Borussia Dortmund and Porto, with Niko Kovac's side perhaps one of the favourites among supporters.
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Gordon characterized his status as a "game-time decision" for Thursday, but players have a knack for sunny prognoses. And when his TD catch with 4 seconds left was confirmed, coach Anthony Lynn sent his offence back onto the field.
However, given the tense relationship between Pogba and Mourinho, Neville felt the midfielder was guilty of a callous piece of opportunism.
Carrick joined the United coaching staff after retiring from playing in May.
"The recruitment over the last years has been erratic, the current management team have had three chances at appointing a manager, they're probably going to get a fourth".
Mourinho's record signing at United, Paul Pogba, has also been one of the biggest misfits at the club, while the likes of Romelu Lukaku, Nemanja Matic and Alexis Sanchez have underperformed under his guidance.
Former Manchester United striker Michael Owen said on Twitter:"Inevitable is the word I'd use. Simply not getting anywhere near enough out of his players".
"Results are obviously an important issue and I dare say that had these been better, and Man U at the top of the table, the board might take a different view".
The United board had seen enough and made a decision to bring in a new manager, and the majority of you agreed.