André Villas-Boas is clinging to his job at Tottenham Hotspur after Sunday's 6-0 hammering at Manchester City prompted the north London club's hierarchy to question whether he remains the manager to establish them in the Premier League's top four.

The Portuguese was cut to evens by bookmakers on Tuesday to be the league's next managerial casualty, with the City result being considered not as an isolated blot but as the most worrying sign of a malaise.

Villas-Boas, who takes his team to Tromso for a Europa League match on Thursday, desperately needs a good result at home to Manchester United on Sunday as he battles a clutch of problems. Those include the perception inside the club that he has sought to blame everybody bar himself for the recent difficulties, from the White Hart Lane crowd and the Tottenham medics to members of the first-team squad. Villas-Boas said that the City loss ought to have provoked shame in the players, which went down badly in the dressing room.

The embarrassment at the Etihad Stadium was keenly felt by the club's chairman, Daniel Levy, and the owner, Joe Lewis, who had initially been angry after the 3-0 home defeat by West Ham United on 6 October and Villas-Boas's hard-luck-story when he read of the defeat.

There had been disappointment at the early-season loss at Arsenal and, the weekend before West Ham, the manner in which Chelsea had reeled Tottenham in to earn a 1-1 draw at White Hart Lane. But West Ham represented the beginning of what has become an intense examination of Villas-Boas's suitability to fulfil Tottenham's ambitions.

The club did not sanction a summer outlay of £110.5m on seven players (including three club-record fees) for a team that would lose at home to West Ham. And, if the ultimate measure of a man is where he stands at times of challenge and controversy, then Tottenham feel Villas-Boas has not distinguished himself.

He took the bold, and possibly foolish, decision after the 1-0 win over Hull City on 27 October to chide the White Hart Lane crowd for how they had created a "very tense, difficult atmosphere". Villas-Boas said it was "like it drags the ball into our goal, instead of the opponent's goal", and added that "this is something that is felt within the squad. It's a feeling that invades us in fixtures like this".

The Tottenham fans are no different to any other London crowd in that they grumble when things are not great and they have only reacted to the football they have seen from their team, which has been cloaked in caution. Spurs have scored nine league goals in 12 matches this season (three of them penalties) and it is not only the supporters, who demand an exciting style, who have become frustrated.

The board has not enjoyed many home matches this season and some of the players have wanted to see Villas-Boas switch from his preferred 4-2-3-1 formation to play with two strikers. Villas-Boas orders his wide midfielders to work hard defensively and so the team have often struggled to commit men in front of the ball.

Villas-Boas reacted surprisingly to the Hugo Lloris controversy, after the goalkeeper had suffered a head injury in the 0-0 draw at Everton on 3 November and played on. When Tottenham's medical staff said that Lloris was unfit to play in the home defeat to Newcastle United a week later, Villas-Boas made it clear that this was their decision rather than his, saying that Lloris had been "clinically and medically" ready to play.

He called for the club to present a member of the medical department before the press to offer a full explanation, which did not happen, and the effect was to make Villas-Boas look isolated and at odds with the doctors.

His comments after the City defeat were badly received in the dressing room and it reinforced the impression that Villas-Boas might be happy to talk up the collective when results are good but he will revert to blaming others in times of adversity.

The criticism from the dressing room is that his highly scientific approach overlooks the human dimension, which is ironic, given that is one of his buzz phrases. The players, technically, ought to have been ashamed after City but, on a human level, would that soundbite not have been better kept behind closed doors? Other managers might have accepted the blame in public, albeit as a diversionary tactic.

Villas-Boas has struggled to manage the transition since the sale of Gareth Bale and the influx, for a second successive summer, of a host of new faces. Some of the existing players have been bumped down the pecking order, which has led to gripes.

Mousa Dembélé, for example, is no longer a first choice after the arrival of Paulinho and Christian Eriksen; Sandro fears that he is behind Etienne Capoue, albeit the Frenchman has been injured and with no left-back having been signed to replace Benoît Assou-Ekotto (on loan at Queens Park Rangers), whose face did not fit, Jan Vertonghen, arguably the club's best centre-half, has been forced to deputise in the position.

Most alarmingly, Villas-Boas has struggled to get the best from the new signings, particularly Erik Lamela who, at nearly £30m from Roma, is the most expensive in Tottenham's history. Given his difficulty in adapting, it was a surprise that Villas-Boas introduced him for his full league debut at City.

Roberto Soldado, the £26m striker from Valencia, has sometimes looked isolated and his impact was always likely to be measured in numbers. He has four league goals, three of them penalties, plus two more in the Europa League qualifier against Dinamo Tbilisi. The hope remains that the new signings will show their true colours once they have acclimatised. The process was never likely to be easy.

Villas-Boas intimated that he turned down Real Madrid and Paris St-Germain over the summer to stay loyal to Spurs and begin a second season at the same club for the first time in his short managerial career. He remains only eight points off the title pace in a congested division but he must urgently address the damaging momentum.