United were beaten 4-1 by Manuel Pellegrini's men, their heaviest away defeat in the fixture since 2004.
Rooney scored a late consolation for United - making him the highest scorer in the derby with 11 - and he was the only player absolved of blame by boss David Moyes.
Rooney told MUTV: "It is not good enough. 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. It is nice to score but it means nothing.
"The most important thing today was the points and we have come away with none."
Next up for United are their old rivals Liverpool in the Capital One Cup on Wednesday night.
The Reds will be bolstered by the return of Luis Suarez, giving an additional twist to what is always a passionate occasion.
Rooney said: "We have all grown up, whether it is Manchester, Liverpool or somewhere else having local derbies.
"It is not nice when you lose one. I have been there as a fan and now as a player. Thankfully we have another massive game against Liverpool.
"It is the ideal game for us. Any game against Liverpool, whether it is a friendly, Capital One Cup or Premier League, is massive.
"We have to try and get the victory so we can put this defeat to the back of our minds."