Palace’s cause was not helped by a 13th-minute red card for Jean-Philippe Mateta, who caught Spurs captain Micky van de Ven on the Achilles with a studs-up tackle.

After referee Michael Oliver’s yellow card was upgraded to a sending-off following a VAR review, it was largely one-way traffic and Tottenham claimed a third consecutive Premier League win with goals in each half by Archie Gray and Jan Paul van Hecke.

It has left Palace in the relegation zone after two wins from their opening seven fixtures under new boss Sage.

Speculation over Sage’s future ramped up after a defeat at home to Newcastle last Sunday and will only increase following this third straight league loss, but the French coach struck a defiant post-match tone.

“Yes, (relegation), it’s a disaster for every club in the Premier League and especially that I have to speak about my club. You know I’m not comfortable with the situation in the table, but it’s a consequence of what we did bad on the pitch,” Sage said.

“My only way to change a thing is to go on the pitch. That is why I talk to the players and I want to be the first on the pitch on Monday. They can trust in me. I will never give up.

“I will do the best session I can do on Monday because now I have the rage to train more because the game I saw was not in line with my conviction.”

Asked for a message to the Palace supporters, Sage continued: “They can trust in me because I will give my life. I am the kind of person who never gives up.”

Roberto De Zerbi was happy with the mature nature of Tottenham’s performance – but called for more nastiness in attack after they produced 34 shots but only two goals in a one-sided contest.

De Zerbi said: “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.

“As I said to the players before the game and in half-time, we can’t forget where we have been two weeks ago.

“Two weeks ago, before the Coventry game, we were last in the table and we can’t forget. I think this is the crucial part, the crucial aspect for this team.

“And then, playing with freedom, enjoying with the ball, attacking many players, no problem, but we can’t forget where we were two weeks ago.”

De Zerbi handed a league debut to 18-year-old Luca Williams-Barnett in the final exchanges and added: “Very young, but a great talent.”