Wayne Rooney has complained of "sloppy goals" and insisted Manchester United must improve quickly following Manchester City's 4-1 rout of the champions on Sunday.

After only 50 minutes of the derby Manuel Pellegrini's side were 4-0 ahead with Rooney's late free-kick, which made him the record scorer of 11 in the fixture, a mere consolation.

"It's not nice to lose to City by four goals to one," said Rooney. "To lose by any score is bad, so we're all really disappointed. 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 were bits of. It just came too late in the game."

After Sergio Agüero opened the scoring on 16 minutes, Yaya Touré claimed the second on the stroke of half-time. This following careless defending from Nemanja Vidic, Chris Smalling and Marouane Fellaini at a corner delivered by Samir Nasri, who later managed the fourth for his side, with Agüero having collected his second two minutes after the break.

Rooney said: "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.

"We knew at 4-0 that we obviously weren't getting back into the game but we had to keep fighting and pressing, trying to make a game of it to show the fans, and ourselves, the pride we have as footballers as it's never nice to lose. I thought during the last 20 minutes we played some good stuff. Had we done that earlier there might have been a different outcome, but it was too little, too late."

Regarding his goal, Rooney added: "It's nice to score but it means nothing. The points were the most important thing and we've come away with none. However, we've got a big game against Liverpool on Wednesday [in the Capital One Cup] so we'll try and forget about today and move on in that game. We've all grown up – whether in Manchester, Liverpool or elsewhere in the world – with local football derbies and it's not nice when you lose one.

"I've been there myself as a fan and as a player, it's never a nice moment. But thankfully we've got the game against Liverpool coming up and it's something we are looking forward to now in the hope that we can get the victory to put this defeat to the back of our minds."