The Red Devils were thrashed in the Champions League by Cesc Fabregas’ men, with Nico Paz playing a starring role.
The result piled the pressure on Carrick, who has now overseen a seven-game winless streak as he continues his first season as the club’s permanent head coach.
The former midfielder held his hands up to the travelling United support in Italy to apologise for the performance, and he faces huge criticism from those on social media, with plenty calling for a change in the hotseat.
Fernandes, who was substituted uncharacteristically in the second half, criticised his manager’s strategy in the dire drubbing.
"It's not the first time, we started on the wrong foot, and they scored very early,” the United captain explained.
Apology: Michael Carrick
PA
“Not much pressure on the ball, not many good movements with the ball, not many things going our way.
"Conceding early makes us go into a game with a mood of defeat, it's difficult to get out of that, trying to be brave, to have the ball and make something happen. If we are not able to do that, it is going to be very difficult to get out of this situation.
"It's a decision from the staff to not press man to man and sometimes leave space behind and try to get the ball, wait for them, but sometimes when you give space to these teams they get confidence."
He continued: "That's on the manager and staff to see, not me. Sometimes you have to be more brave under pressure, take the risk of pressing high and making them uncomfortable.
As you saw with them, the centre-back was coming to mark me in my own half. We needed to do that as a team but we were unable to.
"A team that plays through the middle with small connections, if you give them too much time and space then they can hurt you out wide."