Rooney struck United's only goal as they were thrashed 4-1.
"It's not nice to lose to City by four goals to one. To lose by any score is bad, so we're all really disappointed," he told MUTV.
"The way we conceded the goals, one just before half-time and two straight after, is not good enough. We know we have to improve on that, to stop giving these sloppy goals away and capitalise on some of our good play, which I thought there was bits of... it just came too late in the game.
"It was a blow (City's second) but we still thought we could get back in the game. We've been two down many times before and we came out at half-time ready to get the first goal and that would have been game on. The way in which we conceded two goals so quickly killed the game."