United were beaten 4-1 by Manuel Pellegrini's men, their worst away loss in the fixture since 2004.
Out-manoeuvred in midfield, where £27.5million new-boy Marouane Fellaini was a particular disappointment, the Red Devils conceded three goals in a six-minute spell either side of half-time that left them staring down the barrel of total humiliation.
As it turned out, a combination of City easing off and Rooney grabbing a late consolation meant the damage was not as extensive as had appeared likely.
Still, for a team used to setting such high standards, Rooney knows the performance was not acceptable.
"It is not good enough," the 27-year-old told MUTV.
"We know we have to improve and stop giving these sloppy goals away
"It is not nice to lose to City. It was a bad result and we are all extremely disappointed."
Manager David Moyes excused Rooney from blame, claiming the England man did not deserve to be on the losing side.
His goal - a fourth in three games - means he has now become the highest scorer in derby matches with 11.