The 20-year-old had a hard start to the game but started to become more involved with around half an hour played.
"But I'm going to improve my staff in the performance level and, in relation to the tactical work, I'm going to bring some people that, until this moment, have not come with me yet".
The likes of David de Gea, Paul Pogba, Nemanja Matic, Chris Smalling and Phil Jones were all rested as Carrick was given centre stage after a season of little action.
"I think the Liverpool game is special", Carrick, who joined United in 2006, told ESPN.
Mourinho insists Carrick will not immediately step into the role but hinted he could make another addition to his coaching team.
"It's hard to believe it's not Scholes", chorused Old Trafford throughout, "it's Carrick don't you know".
"He's one of the best".
Manchester United manager Jose Mourinho has admitted he wished he could have coached Michael Carrick earlier in his career after the midfielder hung up his boots on Sunday. It's an unbelievable place to play football.
A tepid encounter was settled in the 34th minute when 36-year old Carrick rolled back the years to find Juan Mata with a delightful pass and the Spaniard squared it back for Rashford to tap the ball in.
In order to traverse a wide chasm such as this, it's going to take a whole lot of squad makeover, as Mourinho said as much today.
"He was injured in the Friday training session and yesterday (Saturday) he couldn't train". The headline news here was Anthony Martial's unavailability because of a muscular problem, with some confusion regarding whether he was seen driving away from the ground just before kick-off. "For 10 months I get asked "why always Lukaku?"
"We spend more time with each other than anybody else in our lives". I know them better than anyone.