The visitors, beaten at Sunderland on Boxing Day, were off to a flying start when they went 2-0 up inside four minutes after Edin Dzeko's quick brace.
The Canaries reduced the deficit through Anthony Pilkington's deflected free-kick before Samir Nasri was shown a red card by referee Mike Jones after 44 minutes for putting his head into the face of Sebastien Bassong.
Sergio Aguero's neat flick made it 3-1 at the start of the second half before Russell Martin's header cut the deficit again.
Dzeko put City back in command at 4-2 after his shot cannoned off a post and in off goalkeeper Mark Bunn, only for Martin's scrambled effort to set up a grandstand finish.
However, Norwich - who had beaten Arsenal and Manchester United at Carrow Road during a 10-match unbeaten run - could not conjure an equaliser as they suffered a third successive league defeat.
Hughton, though, remained positive despite a second home loss in a week after Chelsea ran out 1-0 winners in Norfolk on Boxing Day.
He said: "Manchester City showed why they spend the amount of money they do for the offensive players they have but you cant be 2-0 down so early on and expect to have a good day.
"However, we displayed great character and certainly at 4-3 it seemed it might be going our way but again they showed real good quality.
"I cannot fault the endeavour of the players we have got, so now we will look to go again."