Strains of the old "Glory, Glory" anthem echoed inside the giant stadium as Tottenham Hotspur stepped back from the precipice of the most humiliating relegation in Premier League history.

Spurs players and supporters were in unison at last as they could finally look forward to next season as a top-flight club, victory against Everton on the final day ensuring survival and sending West Ham United into the Championship.

Slowly, a note of dissent was introduced as a giant banner was unfurled by supporters, reading: "Promised Success. Delivering Failure. ENIC out."

The fans who have suffered so much mediocrity were entitled to their outpouring – after all, this was only the third home league win they have witnessed this season, albeit in arguably the club's biggest game in recent history.

For the Spurs players, the instant exuberance was understandable, but embarrassment should have quickly descended on them as they listened to their supporters chanting "We Are Staying Up".

The very sound of those words, the preserve of strugglers, should reverberate through the whole club. Once Tottenham High Road empties of its revellers, the inquest from top to bottom must begin.

This brings us to the move they did get right, which was to persuade Roberto de Zerbi to arrive in an emergency act before the end of the season, rather than wait to see what division Spurs were in before making a commitment.

De Zerbi, by his own admission, has had to be as much a psychologist as coach to coax Spurs to survival. He has done so and deserves credit, with away wins at Wolverhampton Wanderers and Aston Villa, plus this tension-riddled win against Everton, enough to get them over the line.

This celebratory end to a season was also watched by Vivienne Lewis, representing the family who own Spurs, along with her son-in-law Nick Beucher, a key contact with the London-based management.

Non-executive chairman Peter Charrington and chief operating and finance officer Matthew Collecott were also in attendance, presumably poised to work out how and why Spurs have found themselves in such reduced circumstances and how it can be avoided next season.

At least they were spared the pain of seeing Spurs relegated on the day when north London arch-rivals Arsenal were lifting the trophy after their first Premier League title in 22 years. Arsenal's party was taking place across the capital at Crystal Palace.

For now, thanks to De Zerbi's inspiration and the failings of other clubs, Spurs are spared a day of reckoning. Not for long, however, because the temporary elation of fans will soon turn to anger.

How can a club that plays in such a magnificent stadium, has such passionate support and received around £74m by qualifying for the Champions League via that Europa League triumph, end up on the brink of the Championship?

Answer – bad decisions on and off the pitch. Poor appointments. Players playing poorly. At times this season, Spurs have resembled an unmotivated rabble – which is why the frantic pumping of fists and wild celebrations also felt uncomfortable and, yes, embarrassing.

The work must start now, but at least they will have De Zerbi to lead.

The Italian at least realised the urgency of the situation when he said: "It's now around 7pm, and around 8pm or 9pm we will start working towards next season."

De Zerbi added: "Next season we have to build a top, top, top team. We don't have to change too many players in our squad, but we have to bring in some first level players."

He had been out on the pitch before the match, whipping up the Spurs fans.

He was then involved in a heated, angry verbal exchange with Everton substitute Seamus Coleman, celebrating wildly with supporters when Joao Palhinha scored the vital goal – after which he was rugby-tackled by Spurs substitute keeper Guglielmo Vicario.

Spurs were hampered this season by serious injuries to key creators James Maddison, who appeared as a substitute here, and Dejan Kulusevski, but this cannot excuse what has been served up.

Captain Cristian Romero thought better of missing this final game.

Rehabilitating after a knee injury, he had been expected to stay in Argentina to watch boyhood club Belgrano play River Plate in the Argentina Primera Division Apertura final on Sunday.

Will he be at Spurs next season? Will De Zerbi convince Romero's central defensive partner Micky van de Ven to stay at the club?

Van de Ven was looking forward as he said: "I'm really confident. With the right people now here - the right manager - I'm confident. Finishing 17th two years in a row is unacceptable for us."

Spurs have no time to waste in their quest to avoid a repeat.

De Zerbi, who took acclaim at the final whistle, said: "I'm very happy and elated for the performance of my players. They showed they are good people and top players. We played maybe the best game in my time here.

"We played against an Everton side who had a coach in David Moyes that maybe wanted to help keep West Ham up, but I'm sorry, he couldn't do that."

The Spurs team coach was greeted by thousands of fans lining the streets before the game.

"They were fantastic. We had to fight on the pitch to make them happy and proud of us," De Zerbi said. "We need to show more of this spirit in the future."

As the Spurs supporters poured into their favourite watering holes and haunts around the stadium, the inquisition, and plotting for the future, should have already begun inside.

Glory, Glory Tottenham Hotspur? Not this season. No glory here.