The Australian's side were riding the crest of the wave before heading down south for Sunday's Premier League finale, having marched to five successive wins over Coventry City, Brentford, Qarabag, Manchester United and Ferencvaros.
A sixth straight victory looked on the cards against Fabian Hurzeler's side, as Brennan Johnson netted for the sixth game running before James Maddison doubled the visitors' advantage before the break.
However, Hurzeler had evidently roused his troops to the maximum at half time, as Yankuba Minteh immediately cut the deficit in half before Georginio Rutter brought the hosts back on level terms.
The 22-year-old then went from goalscorer to provider, as his delivery found ex-Arsenal striker Danny Welbeck to head in the winning goal in front of a packed away end, completing another fabulous turnaround in Premier League gameweek seven.
Postecoglou: 'I don't care if the players are disappointed'
Prior to Sunday's game, Postecoglou had labelled last season's home defeat to Manchester City as his "worst experience" as a football manager, after his side failed to lay a glove on the champions and some supporters were only too happy to see their side lose, as it meant that Arsenal lost ground in the title race.
However, speaking to the media in his post-game press conference, the 58-year-old suggested that Sunday's capitulation was an even worse feeling, saying: "I don't know if I learned something new but I certainly experienced something new.
"With all these things, straight after a game you're emotional about it. That's probably the most disappointing loss I've had since I've been here, in terms of the way we went about it and it's something I need to assess.
"I'm sure the players are disappointed, but I don't really care about that. They should be disappointed. Our supporters are disappointed, I'm disappointed, but I want them to understand football is not about losing a game of football, that happens. The disappointment comes from us not doing the very basics of what's expected at the highest level from a competitive standpoint.
"We just weren't competitive. We didn't win our duels, we lacked intensity, we didn't deliver the things you need to at this level, the basics of the game, and paid the price for it."
Were Tottenham guilty of "complacency" in Brighton collapse?
Tottenham performed their Expected Goals (xG) metric in the first half, netting twice from 0.95xG while boasting 58% possession, but they could only muster 0.42xG from 61% possession in the second period as Brighton elevated their attacking game.
Asked if Tottenham took their foot off the gas and potentially got overconfident after their string of victories, Postecoglou added: "Not really sure. But wherever it comes from, it doesn't really matter, it's irrelevant. It's unacceptable at the end of the day.
"You can kind of understand that you're not going to win every game. But there's the manner you lose games. And that's the first time since I've been here that we've lost the game in that manner. And like I said, unacceptable.
"Even when we didn't win at Newcastle, we played well and fought hard to the last second to win that game of football. We didn't do that today and every time we've played that's been an element of our game but I didn't see that today. It's for me to address and fix and the responsibility falls at my feet and that's what I need to do."
Tottenham's third loss of the Premier League season leaves them entrenched in mid-table in ninth place, and the Lilywhites return to action at home to West Ham United in the early kickoff on October 19.