Spurs head into Sunday's decisive clash against Everton sitting 17th in the table, only two points above West Ham with a superior goal difference. Victory at the Tottenham Hotspur Stadium would guarantee their place in the top flight next season.
The Italian manager made it clear that survival remains the only focus.
"Everyone has to give something more," De Zerbi told Sky Sports. "From 7pm on Sunday, we can organise and make a plan for next season, considering everything. I am not stupid and I have a very clear vision on what we have to do."
De Zerbi admitted the situation has been more difficult than he expected after arriving at the club during a turbulent campaign.
"It has been a tough experience because I didn't know before my time," he said. "To manage a lot of situations without knowing what happened before me is not easy.
"But I am proud because I created an important relationship with the players, people inside the club and the fans. They do not deserve to stay in this position in the table."
The pressure surrounding Spurs has increased after captain Cristian Romero travelled to Argentina to watch his former club instead of staying with the squad for the Everton match.
De Zerbi defended the defender's absence, explaining it was related to medical reasons, but warned he would not tolerate players putting themselves ahead of the club.
"If I understand there is any player who thinks of himself before the club, I can't be the same Roberto," he said. "But with Cuti Romero, with me, he has been correct from the beginning until now."
Despite the tension surrounding the club, defender Micky van de Ven believes Tottenham have shown enough quality in recent weeks to stay in the Premier League.
Spurs suffered a 2-1 defeat to Chelsea in midweek, but the Dutch defender felt the performance still offered encouragement.
"I wouldn't say Chelsea was a step back," Van de Ven said. "That was the first loss in five games. If you flip the penalty moment, maybe we get a draw. In the last 20 minutes we played good offensive football.
"We've shown our quality lately and how we can play. For a club like Tottenham, it shouldn't be possible that we are in this situation right now."
Van de Ven admitted Spurs only have themselves to blame for being dragged into a relegation fight, but backed De Zerbi's attacking approach to guide them through.
"Since Roberto came in, the positivity and the offensive football have improved," he added. "We just need to stay up. We need the three points against Everton and then leave everything behind us."
Tottenham's home form has been one of the biggest reasons behind their struggles. Spurs have won only two of their 18 Premier League home matches this season, the joint-lowest total in the division.
Van de Ven admitted there was no clear explanation for those poor results.
"The home form hasn't been acceptable," he said. "I seriously have no clue why it has happened, but now we have a massive game on Sunday to change that.
"We're going to need the fans and we know they will stand behind us."
De Zerbi also stressed the magnitude of the occasion, insisting survival would mean more to the club than last season's Europa League triumph.
"After Sunday there is not a trophy or a bonus," he said. "There is something more important - the future and the history of the club, the pride of the players and the dignity of everyone."
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