Five months later on a memorable night in Bilbao, Postecoglou's side did exactly that as they beat Manchester United to win the Europa League and end a 17-year trophy drought for the north London club.
A scruffy goal by Brennan Johnson shortly before halftime befitting a messy game was defended in magnificent fashion as Tottenham ripped up the gung-ho 'Ange Ball' tactics and put 11 men behind the ball to scrap and scrape their way to glory.
Had things gone against Tottenham on Wednesday, it would have been the club's worst season since they were last relegated in 1977 and almost certainly ended Australian Postecoglou's two-season reign at the club.
Instead, he delivered on his promise of always winning a trophy in his second season at a club and whether he is in charge next season or not, the pugnacious 59-year-old will forever be regarded as a Tottenham cult hero.
In the build-up he spoke of changing the perception of a club with a reputation for choking when opportunity knocks.
Against United, they barely crossed the halfway line in the second half as they came under a constant siege but they defended as if their lives depended on it to 'get it done'.
"I know what it is for this football club, it's hard to break that cycle," Postecoglou told TNT Sports.
"I could sense some nervousness because they've been in the situation before but until you get the monkey off your back, you never understand what it feels like.
"Us finishing third (in the Premier League) wasn't going to change anything for this football club. The only thing that was going to change this football club was us winning something."
Tottenham have scored 63 league goals this year and let in 61 -- a bizarre statistic for a club fourth from bottom.
In stark contrast, the knockout rounds of the Europa League have seen Tottenham adopt a more pragmatic approach that did not appear to be in Postecoglou's armoury.
It was a similar story on Wednesday as Tottenham's defence, which at times during the second half was 11-strong, repelled everything that a modest United side could muster.
"You know, when you're in that situation, it comes down to really good organisation, really having a real game plan, and then minimising the moments the opposition have."
Having achieved what the likes of Mauricio Pochettino, Jose Mourinho and Antonio Conte failed to do by delivering silverware, the dilemma now for Tottenham chairman Daniel Levy is whether the former Celtic boss is allowed to continue.
As the fans sang his name on Wednesday he certainly did not sound like a man ready to head off into the sunset basking in the glow of making good on his vow.
"We're still building this team. It's still a very young team," he said. "My thought process of what I've been doing this year is trying to build a team that can be successful for four or five, six years now, but I'm the manager of the football club. That decision is not in my hands.
"I don't feel like I've completed the job yet. We're still building. Those players in there will want to feel this again. They've got it now and they won't want to let it go."
