Carrick urges consistency from 'fantastic' Man Utd after derby win
The Red Devils were inspired by the change in management as goals from Bryan Mbeumo and Patrick Dorgu inflicted a huge blow on City's Premier League title chase.
United also had three goals ruled out for marginal offside calls and were denied by a string of fine saves from City goalkeeper Gianluigi Donnarumma.
"Great start. No getting away from that," said Carrick. "The boys were fantastic."
Just a second win in eight games in all competitions lifted United into fourth in the table ahead of the later kick-offs.