Fernandes pointed the finger at Carrick and his staff after United’s 4-1 defeat by Como in the Champions League, which has piled the pressure on the under-fire head coach.
The Red Devils have now seen their winless run extended to seven games across all competitions.
Carrick was asked about the Portuguese international’s comments when he faced the media post-match.
Apology: Michael Carrick
PA
"We actually half pressed man-to-man in the second half and conceded from that,” the former midfielder responded.
"If you don't run, don't run forward and you don't run back you are not going to win."
When Fernandes was substituted, he was not acknowledged by his manager on a dark day for United.
Nico Paz starred at the Giuseppe Sinigaglia Stadium, scoring two goals, while Joshua Zirkzee netted a late consolation for the visitors, who were deservedly beaten heavily, despite them missing nine first-team players through injury.
Fernandes was replaced in favour of the Dutchman, who made a positive impact off the bench.
United return to Premier League action this weekend when they take on Bournemouth at Old Trafford.
The Red Devils sit 13th in the English top flight, and they have not won in the league since their 5-2 victory over Ipswich back at the end of August.