Spurs were 2-0 ahead and cruising with first-half goals by Brennan Johnson and James Maddison putting them on course for a sixth successive win in all competitions.
But they crumbled after the break as goals by Yankuba Minteh, Georginio Rutter and Danny Welbeck turned the game on its head to leave Tottenham empty-handed.
Speaking to Sky Sports, Postecoglou said his players were guilty of complacency in the second half.
"Disappointing. Frustrated and absolutely gutted with that. Worst defeat since I've been here," the Australian said.
"Unacceptable second half. Nowhere near where we should be. We got carried away with how we were going. We kind of accepted our fate and it is hard to understand as we've not done that while I've been here. We paid the price.
"The problem is we are travelling along too smoothly, football and life will trip you up if you get too far ahead of yourself. It is a terrible loss for us - as bad as it gets."
Tottenham would have moved to the fringe of the top four had they won the game but instead go in to the international break in ninth place with 10 points from their seven matches.
Brighton are up to sixth, two points better off.
"They all go on international duty, the majority of them. They will process it individually and I will process it when everyone gets back," Postecoglou said.
After five league games without a win, Brighton's second-half display sent their fans into raptures.
"My team deserved to win, they worked hard and focused on the things they could control," Brighton manager Fabian Hurzeler said. "I think Tottenham always have a great start. They play with intensity and we were not ready for that.
"We also created chances but defensively we have to improve. We focused on the positive things, the second important thing was to win the duels to build self-confidence. The players worked hard to gain flow and they used it."
