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.

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