Spurs have three successive Premier League wins for first time since February 2025, when Ange Postecoglou was still at the helm.
The game against Palace was effectively over after just 13 minutes when Jean-Philippe Mateta saw a straight red for a rash challenge on Micky van de Ven.
Archie Gray and Jan Paul van Hecke scored the goals to secure all three points for Spurs and take them into the top half of the Premier League.
Speaking to reporters after the game, De Zerbi was clearly delighted, saying: "I'm very happy for the performance, because we showed to be a mature team, with clear ideas.
“We didn't concede a counter-attack, maybe just one in the second half. We created many, many chances. If we want to follow perfection, we have to be more nasty, no?
“That is an individual thing, because if I'm number nine, number 10, I want to score. But I can't say nothing. We are improving the physical condition.
“Tonali today was unbelievable, incredible. We played with two players more. Tonali was the double today."
Sandro Tonali wasn’t the only player De Zerbi singled out for praise.
"But we are improving with Archie Gray, with Robertson, the two central backs very well, to take the command of the game,” he added.
"Mateus Fernandes, another very good performance. Marmoush, Solanke, very well, especially when we lost the ball.
“So it's a clear signal that they were inside of the game. Kudus, Mathys Tel, very well. So I think they are improving and the team are improving. The team is improving."
Young Luca Williams-Barnett also impressed the Italian.
"Yeah but my career is clear. When I work, when I have young, talented players, for me nothing changes.
"I thought it was the right moment for him. Because it is his first game in the Premier League. But his qualities, he is a big, big talent."