Marcus Rashford cancelled out Danny Graham's opener before Zlatan Ibrahimovic netted the winner.
Ibrahimovic and Rashford grabbed the headlines but Carrick produced another masterful display in the middle of the park.
And, with his contract expiring in the summer, Scholes believes the ex-Tottenham star has earned a contract extension.
Paul Scholes believes Manchester United must keep Michael Carrick
Manchester United player ratings against Blackburn
Sun, February 19, 2017
Express Sport brings you Manchester United's player ratings from their FA Cup clash with Blackburn Rovers
Man Utd via Getty Images
1 of 12
Who impressed for Manchester United against Blackburn?
Michael Carrick impressed as Manchester United beat Blackburn
"Michael will be a big miss," Scholes told Republik of Mancunia.
"I hope he’ll get another year.
"He’s been a sensational player for this club.
Zlatan Ibrahimovic scored the winner as Manchester United beat Blackburn
"He doesn’t always get the praise that he deserves really because of the job he does, but the job he does is appreciated so much by the players around him."
Carrick could feature when United go up against Saint-Etienne in the Europa League on Wednesday (5pm).
The Red Devils are aiming to book their place in the last 16 of the competition and lead 3-0 from the first leg.