There are two ways to ask the same question about the Tottenham Hotspur chairman Daniel Levy, the club's owner, Joe Lewis, and the three directors who sanctioned this week's sacking of Harry Redknapp. Do they have delusions of grandeur if fourth place in the Premier League is considered not good enough? Or, to put it more bluntly: what more do they want?

The strange circumstances of Spurs' season have been well chewed over. Redknapp had his team in third place after a series of scintillating performances but a 10-point gap was inexorably clawed away in a patchy run from February. Although Redknapp will not acknowledge it, he and his players were knocked off their stride after his and English football's maddest day, when he walked free from a Southwark court, acquitted of tax fraud on the morning of 8 February. Fabio Capello resigned as England manager in the afternoon and Redknapp, who could have ended the day in prison had the jury decided against him, was installed as the favourite to manage the national team. The Football Association then took almost until the end of the season before unveiling Roy Hodgson as their choice.

Fourth place would have given Spurs a Champions League qualification tie had Chelsea not won the trophy, on penalties, which makes Redknapp's sacking appear harsher still. However unbalanced the season and whatever the irritations for Levy with Redknapp's demands for a new contract, Levy has sacked the manager who took Spurs to their highest positions for years and, in 2010-11, their only ever Champions League season.

When the Tottenham chairman looks up to the clubs who finished above them, he sees Arsenal and Manchester United with income and spending power eclipsing his, and Manchester City too, because unlike Lewis, City's owner, Sheikh Mansour, continues to invest a fortune.

Those three clubs have another feature which Levy and his board must have considered: managerial stability. Sir Alex Ferguson and Arsène Wenger have built empires at United and Arsenal and survived periods – although Ferguson's was more than 20 years ago – when their boards considered replacing them. Roberto Mancini's tenure is much shorter and more insecure but Mansour's executives still supported the Italian when City wobbled badly at Arsenal and José Mourinho was said to be looking at properties in England. Stability, with the right manager, is a key to football success and Spurs have had too little of it. The last manager to work even as long as Redknapp's four years at White Hart Lane was Terry Venables, from 1987 to 1991, 21 years ago.

Levy's performance in manager recruitment has not been consistent. Jacques Santini and Juande Ramos flopped while Martin Jol was a solid leader before Redknapp arrived in October 2008 and set Tottenham on the route to relative excellence. There are more ways for things to go wrong than for a new manager to improve on a fourth place.

In the Premier League, performance roughly equates to financial power. In that Darwinian environment, Redknapp surpassed expectation. Sheikh Mansour spent around £1bn to win City the Premier League. United, frayed by the Glazers' massive debt burden, still had an income of £331m in 2010-11, the year of clubs' most recent published financial accounts, and serviced a wage bill of £153m. That is £62m more than Ferguson spent paying players than the £91m made available by Levy to Redknapp. Arsenal, whose superiority Spurs feel most keenly, turned over £256m at the Emirates Stadium, Wenger spending a relatively modest 48% of that on wages, still £124m, substantially more than their north London rivals.

Redknapp steered his team to finish above Chelsea last season, whose turnover and backing by Roman Abramovich far exceeds that of Spurs and Liverpool, whose wage bill in 2010-11 was £135m.Tottenham's 2010-11 turnover was £163m, up from £120m the previous year largely due to participation in the Champions League. Levy is frustrated to see such money now beyond reach but surely it is unrealistic of a chairman working for Lewis – billed as a billionaire but who invests little of his own money – to expect Champions League football.

The size of a club's stadium has long determined financial power and Spurs have talked a great deal about a new stadium without actually building one. White Hart Lane's capacity is 36,534, less than half that of Old Trafford's 75,769. The comparison which hurts, though, is with Arsenal, who remain the only top club to have successfully built a stadium themselves – not with public money like the former 2002 Commonwealth Games stadium which Manchester City occupy – in the modern era. John Henry, Liverpool's American owner, pointed that out in an illuminating interview with The Anfield Wrap website this week, explaining again why he prefers to expand Anfield than build a new stadium at Stanley Park.

Levy talked first of enlarging White Hart Lane, then building a stadium nearby, then lost the bid to take over the Olympic Stadium site, before returning to the Northumberland Development Project. This promises to build an expanded, 56,000-seat ground on White Hart Lane, and public money is promised to aid local regeneration.

Yet despite all that talk, the tough work necessary to build Tottenham into Champions League regulars, remains just that – talk. There was nothing empty, however, about Redknapp taking Spurs to fourth, fifth and fourth again in the past three seasons. And he did it without breaking Levy's bank, by extracting excellence from his players – until the upset over the England vacancy. His replacement will be hard pressed to do better.

The suspicion remains that sacking the manager is, for Levy, displacement activity, a distraction from working out how to achieve the very thing that would convert Tottenham into bona fide Premier League contenders alongside Arsenal, City, United and Chelsea – to build the stadium Spurs have spent so long talking about.