Ironically, this essential win occurred in a competition the 59-year-old manager hadn't prioritized, achieved through a performance deviating somewhat from the high-risk approach that has tested local support in North London.
It wasn't a complete abandonment of Postecoglou's principles, but rather a noticeable compromise. Tottenham's average possession start was 31.6 meters from goal, their fifth lowest this season across all competitions, compared to their season average of 35.8 meters. The team also made only 44 passes in the attacking third, significantly fewer than the 83 against Liverpool last month and 77 in the previous round against Manchester United.
Rodrigo Bentancur's early head injury, which saw him stretchered off and taken to hospital in what Postecoglou described as "a quite distressing sight," likely disrupted their rhythm. Spurs later confirmed he was conscious and speaking.
A depleted squad due to injuries and the strength of the opposition were also contributing factors. The first half, unusually for Spurs, was relatively uneventful. Postecoglou's demeanor also differed from his usual stoicism; he was unusually expressive on the sideline, even dropping to his knees when Pedro Porro failed to capitalize on an early second-half error by Alisson Becker.
Dominic Solanke's 77th-minute goal was disallowed after a VAR review for offside, confirmed by in-stadium refereeing announcements. Lucas Bergvall's winning goal nine minutes later ignited jubilant celebrations that continued after the final whistle, as Postecoglou celebrated with loved ones and enjoyed the festive atmosphere surrounding a result that moves Spurs closer to their first trophy since 2008.
Postecoglou, usually composed, has been under considerable pressure due to a recent run of four wins in 15 matches.
"It has been an emotional time," he admitted. "I am a human being. We are in positions of responsibility, but we are still human beings and we react to things.
"I don't like that people working hard for this club haven't had that feeling of victory. I don't feel great about our supporters not having that feeling.
"It weighs heavily on me. It is my responsibility. So I am a little bit more emotional than I usually am, but that probably means I do care."
After a difficult month for Postecoglou, the possibility of a cup final could be the much-needed focal point for Spurs.
This was only Liverpool's second defeat under Arne Slot, achieved by a makeshift Spurs team featuring debutant Antonin Kinsky in goal, teenage right-back Archie Gray at centre-back, and out-of-favour Djed Spence. Spence performed significantly better against Mohamed Salah than in the 6-3 Premier League defeat 17 days prior.
While it appeared pragmatism had influenced Tottenham's approach, Postecoglou attributed it to circumstances.
"People said my midfield setup was a little bit more conservative, but that's because I only had three midfielders to choose," he explained. "Liverpool don't allow you to play the same way as other teams, and our players are playing every three days without rest.
"Liverpool brought on significant talent at the end. I couldn't do the same. Yet, the guys out there are consistently performing. Maybe we are not as dominant as we want to be, but there's good reason, not through lack of trying or different intent."
Liverpool made rotations before the game, but Slot introduced Trent Alexander-Arnold, Luis Díaz, and Darwin Núñez among his five substitutions to try and secure a first-leg advantage. Alexander-Arnold had a shot cleared off the line, and Núñez came close twice, but Spurs scored late, benefiting from a questionable decision by Stuart Attwell to not give Bergvall a second yellow card for a late tackle on Kostas Tsimikas.
Adding to Liverpool's frustration, Tsimikas was waiting to return to the pitch when Solanke set up Bergvall, who scored past Alisson.
"I don't think there is any debate about that," Slot said regarding whether Bergvall should have been sent off.
Given Liverpool's strong form under Slot, they remain confident of overturning the deficit on February 6.
Both teams have seven games before then. Liverpool will focus on their Premier League title challenge, while Tottenham's schedule includes the North London derby against Arsenal and difficult away games against Everton and Brentford, all while the transfer window remains open.
But for Postecoglou, there is now a point of optimism: a second leg where they have a narrow advantage, offering hope during a challenging month. It will require another huge effort to reach Wembley, but Postecoglou will feel revitalized for the challenge.