Manchester United supporters vented their anger at the former manager Sir Alex Ferguson at the end of the shambolic 3-0 derby defeat to Manchester City at Old Trafford. In the first signs of open revolt at David Moyes, fans furiously questioned Ferguson's decision to appoint the Scot as his replacement.

With Moyes also receiving verbal abuse from supporters and stewards being asked to guard "The Chosen One" banner that hangs at the stadium's Stretford End after the 167th Manchester derby, the ire shown towards Ferguson, who is a club director, will cause serious questions at boardroom level.

Moyes has consistently spoken of how the support has stood by him throughout his overseeing of a dismal title defence. This defeat guarantees United will end with their poorest ever points tally in the Premier League era, with their previous lowest being 75.

City took only 43 seconds to take the lead through Edin Dzeko, who also scored again in the 56th minute, before Yaya Touré sealed United's humiliation with a third for City at the end. That provoked fans to target Ferguson as he sat in the directors' box at the final whistle.

The 72-year-old was the driving force in Moyes being appointed as his successor at the end of last season, with the former Everton manager being summoned to Ferguson's house to be offered his job.

While the loss made it six home defeats in the league for the first time since the 2001-2 season to leave United 18 points behind the leaders, Chelsea, and 12 from a Champions League berth, Moyes refused to blame his players. Asked to explain how a squad minus only the retired Paul Scholes has gone so far backwards this year after winning the title by 11 points, the manager said: "I take responsibility. I have to be the one who plays them, picks them and that is what it is. I think there are a lot of really good players there, some can play better, but there are a lot of really good players in the squad, a lot of international players and players who I think on their day can be a match for most players."

Sir Alex Ferguson watches Edin Dzeko help Manchester City to a 3-0 win, which heaped more pressure on David Moyes. Afterwards, stewards were on hand to protect a banner. Photograph: Paul Ellis/AFP/Getty Images, Peter Powell/EPA, Carl Recine/Action Images

Of the defeat to City, which means they have now been defeated by their city rivals three consecutive times at Old Trafford in the league for the first time in more than 40 years, Moyes said: "We never gave ourselves a great opportunity to get into the game. Manchester City started really fast and conceding a goal after 30-40 seconds made it difficult. We had to try and make sure we got through that 10-15 minute period. After that we weathered it and got ourselves back into the game and finished the half quite strong. The key to it was not to concede a second goal so we could always give ourselves a chance [to get] back in there.

"I didn't think we started the second half well. We brought pressure on us by our play and in the end we conceded a corner just before that and there was another one and then that led to the second goal. It was obviously poor marking and we should have done much better.

"I just think we never came out of the blocks. You prepare the players, you warm them up, you do all the things to have them ready but we just never started. It gave them a real big lift to get a goal so early on."

In a comment that may further anger fans, Moyes stated that City are the side he wants his United team to emulate. "I think we've played a very good side and it's the sort of standard and level we need to try and aspire to get ourselves to at this moment in time," he said.

City are now only three points behind Chelsea with two games in hand. Yet Manuel Pellegrini refused to concede that it is his team's title to lose. "No I don't think so," said the manager. "The title race continues, we continue fighting with all the other three – Arsenal, Chelsea, Liverpool. We have two games postponed but we have to win those two games. Tomorrow I start thinking about Arsenal [who City visit on Saturday] and then I think about the end of the season."