The vitriol aimed by some Manchester United fans at Sir Alex Ferguson for appointing David Moyes may signal the endgame of his tenure as manager.

Manchester City's 3-0 win at Old Trafford on Tuesday followed the 3-0 trouncing by Liverpool in United's previous home league game to move the conversation on to the point all managers dread.

After open revolt against Moyes began at the stadium, the question now being widely asked is: "How bad does it have to get before Manchester United sack David Moyes?" Or, "Will he really survive until summer if the hidings continue?"

It was a question those at the top of the club did not answer when it was posed on Wednesday morning.

Football is the ultimate results game, and this season those of Moyes have stunk. United have 51 points compared with 74 at the same time last year. They have never previously had fewer than 60 at this stage. Old Trafford has mutated from the fortress opponents hoped to escape from with only a minor beating to a destination most desirable. Under Moyes, United have fewer home points (21) than Norwich City and Hull City, with their count of 18 goals the same as Fulham and Cardiff City, who prop up the table.

The unwanted statistics (and broken records) keep coming. The capitulation to City meant six home league defeats, which has not happened since the 2001-02 season, and the first time the club from across town had recorded three consecutive league wins over United in more than 40 years. It also marked the first time the champions have lost 10 games in a season in the Premier League era. West Bromwich Albion had not won at Old Trafford since 1978 before September's 2-1 victory, a sequence-breaker followed by Everton's 1-0 triumph there in December (this had not happened since 1992), which came before Newcastle ended 41 years without a win on United's patch the same month.

To be a top-line team and have one awful performance during a season is hardly news. To have three in quick succession is way past unfortunate. Reverses to Olympiakos, Liverpool and City have shone a light on the inadequacies of the Moyes project, with the chief concern that in late March of his debut year there is no sign of improvement.

The reverse is true. United are speeding backwards at a rate of knots. Going down 2-0 at Olympiakos, the Champions League last-16's easiest opponents, then 3-0 and 3-0 to United's closest rivals at home has brought Moyes to the point where his job expectancy is discussed in game-to-game terms.

The United buzzwords of stability and longevity symbolised by the six-year contract handed to the 50-year-old were forgotten on Tuesday as the thus-far loyal fans snapped and Ferguson was abused for anointing Moyes his successor.

This was the scene after Ferguson sat in the directors' box and witnessed Edin Dzeko needing 43 seconds to start a rout that could have been more painful.

A further strike from Dzeko before Yaya Touré completed United's misery at the close had members of the faithful using industrial language to ask Ferguson why, precisely, he had decided Moyes was the man to take over.

The mood inside Old Trafford turned from defiant stoicism to open anger. The lift given by the 3-0 win that overturned Olympiakos's advantage and took United into a Champions League quarter-final with the holders, Bayern Munich, and Saturday's 2-0 victory at West Ham United evaporated in the seconds City took to cruise forward and establish a 1-0 lead.

The sense is that the defeat to Manuel Pellegrini's team may prove fatal. One popular theory was that as long as Moyes retained the backing of the hardcore supporters he would survive.

Understanding this, he has continually praised their unwavering support despite the shocking home form – Swansea City beat United at Old Trafford in the FA Cup – and the taking of only five points from the big four of Arsenal, Chelsea, City and Liverpool, before Pellegrini's side arrived.

In the United programme for the 167th derby Moyes moved to shore up his core constituency. Yet it read more like a plea for them not to turn on him and to the owners, the Glazers, to remember the mantra about managerial longevity.

Moyes wrote: "Our thoughts are well and truly on the future and our planning is already well under way, not just for next season, but for many seasons to come. During Manchester United's long periods of dominance in the last two decades, which brought unparalleled success, many other clubs had to undergo periods of turnaround and they knew tough times when things were not going well for them. They looked to change lots of different managers and players, all the while trying to find ways of keeping up and competing with United."

The first public display of disquiet was the fans catching up with the mood inside the club, where the hierarchy were first taken aback by the abject showing in Athens. The performance of Moyes's side that evening at the Karaiskakis Stadium was so incongruous that to find a precedent was difficult.

That the defeat to City was the tipping point regarding Moyes for some Old Trafford regulars is recognised within the boardroom as understandable, especially following the defeat to Liverpool.

Publicly United continue to back the manager. Yet another dismal outing when Aston Villa visit on Saturday lunchtime would further cast Moyes as a moribund man walking towards what could prove the final reckoning – the meeting with Bayern on 1 April.

The Glazers and their man on the ground, Ed Woodward, the executive vice-chairman, have shown admirable patience. Once this goes expect Moyes's removal to happen quickly and ruthlessly.