The Geordie is happy working for the caretaker manager.
He told ESPN: “It's gone as well as anyone could have hoped for.
"The start we had at Cardiff was essential and then to go to Tottenham and win was massive. It's just snowballed from there."
Carrick also admitted he wanted Solskjaer to stay for his own interests.
"He'll have to stay because I need to keep my job!" he said. "I don't think you'll get many Manchester United fans or players who will say otherwise to be honest."