Fernandes scored as the Red Devils beat 10-man Tottenham 2-0 on Saturday to solidify their place in the Premier League's top four.
Carrick is yet to lose in seven games during two spells as interim United boss.
The former midfielder insisted before this weekend that the United hierarchy cannot rush into a decision over who will be the club's next permanent manager.
However, the results and performances since Ruben Amorim's departure last month are making a strong case for the former Middlesbrough boss to be handed a deal beyond the end of this season.
"Carrick came in with the right ideas, giving the players the responsibility and freedom on the pitch," Fernandes told TNT Sports.
"I was sure he would be a great manager and he is showing it. We hope we can help him even more.
"Everyone understands the pressure of playing for this club, everyone knows the expectations around it. He knows what it means for this club to win. It adds something special to the team."
Victory takes United to within two points of third-placed Aston Villa and opens up a cushion on the chasing pack for a place in next season's Champions League.
A place in the top five is likely to secure a spot in next season's Champions League due to the strong performance of English sides in European competition this term.
United move five points clear of sixth-placed Liverpool, who host title-chasing Manchester City on Sunday.