Carrick signed a one-year contract extension at Old Trafford earlier this summer, but is yet to feature in the Premier League under Jose Mourinho.
The 35-year-old was the standout performer for United against Northampton Town in the EFL Cup on Wednesday though, playing the full 90 minutes and scoring the opening goal to help the Red Devils to a 3-1 victory.
"We saw the other night, I know it was against Northampton, but Michael ran the game," Robson told talkSPORT.
"He's a real intelligent passer of the ball and he knows where to be on a football pitch. For me, Michael would always be in my team."