Conor Gallagher struck from long range after 12 minutes for his first Tottenham goal since joining from Atlético Madrid in January, and Richarlison headed home a second on 25 minutes to effectively end the contest as a spectacle at a Villa Park where the home side made seven changes ahead of Thursday's Europa League semi-final second leg against Nottingham Forest.
Emiliano Buendia headed a consolation in stoppage time but it was a comfortable afternoon for Spurs, whose second consecutive win — following the 1-0 victory over Wolverhampton Wanderers last weekend — moves them a point above third-bottom West Ham United with three games remaining.
De Zerbi was satisfied with the performance but refused to allow his squad to settle.
"Especially in the first half, we could have scored more goals than two. We didn't concede any chance to score and played very well. The right spirit and behaviour on the pitch. I'm pleased with the performances."
He acknowledged the mood at the club before the recent turnaround but made clear it cannot become a reference point for complacency.
"I knew my players were very good before this game. We have not to forget the situation before Wolverhampton. The season is not finished yet and we cannot be happy just for these two wins. We have to keep working with the same mentality."
His message for the week ahead was pointed.
"Now I don't want to hear the positive voice. We have to stay focused for the next game. Football can change week-by-week and we can't forget the position in the table and what we felt before the Wolves game. We have to push again."
Spurs face Leeds United on Monday evening in what could prove the most consequential fixture in their season. Leeds, level on points with the visitors in 17th, are fighting for their own survival and in strong form. De Zerbi acknowledged the quality of the opposition.
"Leeds are playing very well. They deserve to be in this position in the table. We can't forget what the situation was before Wolverhampton — before that it was a very sad situation. These memories have to stay in our head every day, especially this week after this win."
Spurs' injury list remains severe, with Xavi Simons, Dominic Solanke, Guglielmo Vicario, Cristian Romero, Mohammed Kudus and Dejan Kulusevski all unavailable. The squad that won at Villa Park did so without six established first-team players.