Joao Palhinha scored the only goal for Tottenham in their 1-0 win against Everton at Tottenham Hotspur Stadium.
De Zerbi admitted relief and pride as Spurs confirmed their top-flight status, saying the victory was fully deserved after a season of struggle.
"I'm happy. We deserved this day, this win, everything," he said. "I think we deserved to stay up. In the last seven games we got 11 points and maybe we deserved more. The players showed fantastic spirit, behaviour and quality, especially in the first half."
The Italian coach insisted the focus must now shift quickly to rebuilding the squad. While he believes much of the current group can remain, he called for key additions to raise the overall level.
"We have 10, 11, 12 players good enough to stay," he explained. "But we need first-level players because we suffered too much. We cannot suffer like this again."
De Zerbi also praised the connection with supporters, rejecting criticism of the fans and highlighting the atmosphere around the stadium on a tense final day.
"The fans were fantastic," he said. "The stadium is incredible. I want next season to make them happier and compete for something better."
He reserved special praise for goalkeeper Kinsky, revealing he once considered making him captain to support his confidence during a difficult spell, while also commending veteran keeper Vicario for his professionalism.
"I thought about giving Kinsky the captaincy just to show we are like a family," De Zerbi said. "But he didn't need it - he has strong character."
Several players were singled out for their impact in turning the season around, including Radu Dragusin, Rodrigo Bentancur, Joao Palhinha, Ben Davies, Djed Spence, Micky van de Ven, Richarlison and Archie Gray.
Looking ahead, De Zerbi made clear the survival battle must never be repeated.
"We must learn from this," he said. "Every training session, every game must feel like this one. If we remember that, we will be stronger."
Chelsea's season ended in frustration as they slipped to a 2-1 defeat away to Sunderland, a result that confirmed a 10th-place finish and the absence of European football next season.
Liverpool legends Andy Robertson and Mohamed Salah admitted it was one of the hardest days of their careers after saying farewell to Anfield following the Reds' 1-1 draw with Brentford on the final day of the Premier League season.
Manchester City manager Pep Guardiola delivered an emotional farewell speech at the Etihad Stadium on Sunday after taking charge of the club for the final time, admitting he was overwhelmed by the love shown to him by supporters.
Sunderland will make their return to European football for the first time since 1973 following a memorable 2-1 victory over Chelsea on the final day of the Premier League season.
