Spurs sit 17th in the Premier League with just two points from four matches and are yet to score a goal this season, an alarming return given the roughly €370 million spent in the transfer market over the summer and back-to-back 17th-placed finishes in the two previous campaigns.
De Zerbi had tried to play down the situation in his own way after a goalless draw with Everton at the weekend, pointing to Tottenham's defensive record in his post-match remarks.
"In Italy, with two clean sheets in the last two matches, I would be the best coach in the world," De Zerbi said. "No? What would the Gazzetta dello Sport write? Two clean sheets. I arrived last season when the mess was at this level [he raised his hand to illustrate]. It was a mess. Now, let me explain, I'm sorry for the results, but today we played as a team. Today and against Nottingham."
That response did not sit well with 1998 World Cup winner Dugarry, who unloaded on the Tottenham head coach during his regular slot on RMC Sport.
"He signed for five years, the heist he's pulling off, without even wearing a balaclava," Dugarry said. "It's a crazy situation! And over there, they pay you every week in England, so you can just take it. It's wonderful, what he's doing. He's proven so much in football that he was supposedly incredible.
"I've never understood what this man's real level actually is. People explain to me that he did well at Brighton, at Sassuolo, and I don't know where else. For me, that's not an absolute reference for coaching big clubs, he's had his chance. Right now, he's struggling to take it."
Dugarry went further still, questioning the way De Zerbi has conducted himself in public since arriving in England, including a touchline exchange with substitute Mathys Tel during the Everton match.
"The comments he's made about this player, about that player, he's completely lost the plot, this man," Dugarry said. "It's staggering to have so little self-awareness about what you're saying. Is there nobody around him who's going to tell him, 'just be quiet'? He's completely off in his own world."
Tottenham's struggles have left De Zerbi under mounting scrutiny just months into a five-year contract signed after he arrived last season with the club fighting to beat relegation, a battle Spurs ultimately won on the final day of the campaign.
Dugarry's intervention adds to a growing chorus of criticism facing the Italian, whose managerial CV before Tottenham consisted of spells at Brighton, Sassuolo, Shakhtar Donetsk and Marseille.
While De Zerbi is credited with an attractive, possession-based style of play, his critics point to a lack of major trophies as evidence he has yet to prove himself at the level now expected of him in north London.