Carrick has United sitting in third place on the Premier League table after taking over from Ruben Amorim in January.
Former United captain Robson told the club's website: "Michael’s done great, because at United, when he’s been interim manager, he’s had eight wins and two draws (before Newcastle away).
"When you look at the last time he was here (in 2021), he beat Villarreal away in Europe, came back and drew with Chelsea, at Chelsea, who were flying at the time. Then he beat Arsenal at Old Trafford and we all see what he’s doing now.
"He’s doing it quite simply, but that’s because he’s got a great football brain. He went back to a back four, because the back three wasn’t suiting the boys. He put Luke (Shaw) back to left-back, which is his favourite position.
"Kobbie (Mainoo)’s come back into midfield – a young lad with great ability. He was only out of the team because he got a bit rusty with injury.
"The balance of the team is back and the results show that. So Michael’s done a great job, so far, and I hope he keeps doing it this season. I hope he achieves the task of getting us into the Champions League, but he’s doing great at the moment."