Jean-Philippe Mateta scored the only goal of the game just after the half-hour mark at Selhurst Park to seal Palace's first Premier League win of the season. Spurs defender Micky van de Ven was easily dispossessed deep in his own half before Daniel Munoz's cross found Ebere Eze. He in turn set up Mateta, with the Frenchman on target with a low finish.
Defeat by one of their London rivals left Spurs eighth in the table, with Postecoglou's men now having lost four of their nine league matches so far this term. Inconsistency has been a perennial problem for Tottenham, last crowned champions of England in 1961, with Postecoglou accepting a Spurs side missing injured captain Son Heung-min had been outfought by Palace.
"It was one of those games with a lot of stoppages and battles and they (Palace) ended up winning a lot of them and coming out on top," Postecoglou told the 'BBC'. "There was a lot of disruption and it was hard to get any fluency. They did better than us.
"It turned into a game they were thriving on and we should have dealt with it better. It was a poor goal to concede, it had nothing to do with playing out from the back. That can happen."
The Australian added: "I'd be very surprised if they (Spurs supporters) were happy right now. Why would I be happy? If I'm unhappy then they'll be unhappy."