Mark Hughes angrily criticised the timekeeping at Old Trafford after Michael Owen's dramatic winner, almost 5½ minutes into stoppage time, gave Manchester United a controversial 4-3 derby win and left Sir Alex Ferguson revelling in the misery of the team he described as "our noisy neighbours".

Hughes was furious that the referee, Martin Atkinson, allowed the game to continue for so long after the fourth official signalled four minutes of added time and his anger was exacerbated by Ferguson's provocative remarks, the United manager claiming his team should have won 6-0 before belittling Manchester City even further.

"It's been unusual for us to accept that they [City] are top dogs in terms of media attention but, you know, sometimes you have a noisy neighbour and you have to live with it," Ferguson said. "You can't do anything about them if they keep on making noise but what you can do, as we showed today, is get on with your life, put your television on and turn it up a bit louder. As far as the players are concerned, they showed their playing power today and that's the best answer of all."

Hughes could not disguise his displeasure when he was made aware of those remarks but his main grievance was with the amount of stoppage time. At the final whistle he pointedly held out four fingers to Atkinson and, having watched the game's final stages on video, his mood was even worse.

"The fourth official [Alan Wiley] tried to give me an explanation but it didn't sit comfortably. He said he [Atkinson] had added a minute-plus because of our goal celebration [after Craig Bellamy had made it 3-3] but they got it wrong. We feel robbed."

The official time for Bellamy's goal was 89 minutes and 54 seconds and Hughes continued: "We scored right on 90 minutes and the board was already up for four minutes. We have since timed it from when we scored to when the game kicked off again and it was 45 seconds. They [United] actually scored after 95 minutes and 26 seconds, so he has obviously played too much time – and he actually went on to play 97 minutes in total.

"I just want an explanation. I'm not going to question his integrity, I just want an explanation why he added seven minutes and, if he can give me a good reason, I won't have a problem, but I just can't see where he got that time. It would be nice to get an explanation, though I doubt I will get one."

Hughes noted that Old Trafford had a reputation for matches running well over the allotted time. "Historically it has happened before," the former United player said. "I was in teams here who had that benefit and I never thought it was an issue because I actually thought we had a bad time by referees. Since I left I have probably changed my view."

Ferguson disagreed. "The four minutes went up and then they scored their goal. I don't know how long it took for them to celebrate but it took some time and that's where the added time came from. But at the end of the day we have had a fantastic performance.

"I mean, really, what could the score really have been? We made three horrendous mistakes which you don't even half associate with our team and it kept them in the game. We could have scored six or seven. The fact we made the mistakes probably made it the best derby game of all time, so you're left wondering, would you rather have won 6-0 or won the greatest derby game of all time? I would rather have won 6-0."

"Maybe he feels the need to say that but I don't think he needs to," Hughes responded. "I also feel we had a chance to go into the lead [at 1-1] when Carlos Tévez hit the post. He was fouled by Patrice Evra and it should have been a penalty but the referee missed that as well."

Hughes's mood was not helped by the manner in which United celebrated the winning goal, complaining that the unused substitute Gary Neville had "run on like a lunatic". Neville ran along the side of the pitch to celebrate in front of the City supporters and Hughes described his former team-mate as "over-excitable".

It was the tone of an afternoon in which Ferguson and Hughes could also be seen exchanging angry words on the touchline. Asked later whether United's "noisy neighbours" would be quieter for a while, Ferguson replied: "Well, they'll always be noisy."