The Italian, appointed at the end of last month following Igor Tudor's interim spell, saw his side remain in the relegation zone after a damaging loss on Sunday.
Spurs were undone by Nordi Mukiele's deflected second-half strike, leaving them two points adrift of safety with six matches remaining.
Tottenham, who had not won a league game since late December, struggled to turn possession into goals despite a promising first half. De Zerbi remained focused on the bigger picture.
"We have to work for one win because with one win we can change everything this season," he said. "The players have quality, but we have to believe more in ourselves. The crucial part is to win one game."
He also made a striking assessment of his squad's mindset, suggesting their issues were psychological rather than tactical.
"I can be a big brother, a father - they don't need a coach," De Zerbi explained. "They don't need to improve football. They will play better once we reach a different level of confidence."
A potential turning point slipped away when a penalty awarded to Spurs was overturned after VAR judged that Randal Kolo Muani had not been fouled.
For Sunderland, the result marked continued progress under Regis Le Bris. His side secured a third win in four matches, climbing to mid-table after a disciplined display.
"In this industry you have to win, and it is about finding a way," Le Bris said. "It was a tough game to prepare for, but the players were adaptable and proactive."
He added: "It was about key moments. The goal came from a deflection, but it still counts. Small details make the difference at this level."
Tottenham now faced a daunting run of fixtures, with confidence fragile and time running out. For De Zerbi, the message was clear - belief, not tactics, could decide their fate.