Spurs blew a 2-0 lead established by Brennan Johnson and James Maddison to lose 3-2 at Falmer stadium as Brighton fought back by goals from Yakuba Minteh, Georginio Rutter and Danny Welbeck.
"It was disappointing and I’m absolutely gutted with that," said Postecoglou.
"It's an unacceptable second half - we were nowhere near where we should be. Maybe we got carried away with how we were going.
"We kind of accepted our fate and it's hard to understand as we've not done that while I've been here. We usually fight for everything, and when you don’t you pay a price."
Postecoglou also snapped: "Maybe things were travelling on too smoothly. Football and life will trip you up if you get too far ahead of yourself and that’s what it looked like in the second half.
"It’s a terrible loss for us, as bad as it gets, and there’s only one way to fix it and that’s my responsibility.
"We lost all our duels, we weren’t competitive and if you're not competitive, irrespective of what you do tactically, it is not going to work."