Spurs brought in the former Brighton and Marseille boss at the end of last month in a last-ditch bid to save themselves from a catastrophic relegation.
But the Italian failed to inspire his team in a tricky baptism at Sunderland, and his team remains in the drop zone.
Tottenham, playing under their third manager this season, are without a Premier League win since late December as they contemplate the nightmare of a first relegation from the English top flight since 1977.
The visitors looked bright in the opening stages and were awarded a penalty that was subsequently overturned by VAR.
De Zerbi’s team were grateful to goalkeeper Antonin Kinsky, who was out quickly to smother a Brian Brobbey shot at point-blank range shortly before half-time, while Robin Roefs denied Dominic Solanke at the other end.
Sunderland took the lead courtesy of a huge slice of luck on the hour, when Nordi Mukiele’s shot took a massive deflection off Micky van de Ven and looped into the goal.
De Zerbi made three changes, bringing on Joao Palhinha, Pape Matar Sarr and Mathys Tel and then lost captain Cristian Romero to injury.
Spurs pushed hard for an equaliser late on, but Roefs tipped over a powerful Pedro Porro effort in stoppage time to ensure the win for Sunderland.
Tottenham, who parted ways with interim boss Igor Tudor at the end of last month, are two points behind 17th-placed West Ham and have six games left to save themselves from an almost unthinkable relegation.
They are the ninth-wealthiest club in the world, according to Deloitte’s latest rankings, underlining the extraordinary nature of their predicament.
Relegation rivals Nottingham Forest held Aston Villa to a 1-1 draw at the City Ground and remain one point above the Hammers.
Unai Emery’s Villa, chasing a Champions League spot next season, took the lead courtesy of a Murillo own goal.
Forest were level later in the first half when Neco Williams finished smartly from outside the box.
Jean-Philippe Mateta scored twice, including a stoppage-time penalty, as Crystal Palace came from behind to beat Newcastle 2-1 at Selhurst Park.
