In fairness, a match at Ibrox was never going to feel like a homecoming for a man who won five major trophies with Rangers' archrivals Celtic before making the move to north London 18 months ago.
Postecoglou still garners devotion from one half of this city; Celtic fans bought wholeheartedly into his "we never stop" mantra -- but the Rangers fans filtered through the turnstiles of their historic ground, braving the bitter cold, hoping to watch their team land a knockout blow to the 59-year-old's Spurs' tenure.
But for Postecoglou's use of his substitutes' bench in the second half, the home fans would have seen their wish fulfilled as the Premier League club was bested in large parts by the third-best team in Scotland that had one eye on an Old Firm clash on Sunday in the Scottish League Cup final.
Support for Postecoglou is also in short supply among Spurs' travelling fans, who offered a muted response to their team when the 1-1 draw was confirmed at full-time here. One week ago, some of them were involved in a heated exchange with the Australian coach after the defeat to Bournemouth.
"As expected, they're always difficult to play against here at Ibrox, particularly on European nights," Postecoglou said at a post-match news conference.
"Just the nature of the contest. The atmosphere. Not many teams come here and win. So you kind of expect it to be a tough game and we weren't anywhere near our best. That's fair to say.
"But at the same time, we're in a sort of period of games where we are kind of grinding through at the moment with obviously with a fairly depleted squad and we're asking players to sort of get up week in, week out. So in the context of that, in the end, I think it was a good outcome for us."
The draw leaves Spurs' hopes of finishing in the UEFA Europa League's top eight, and thereby avoiding the playoff round, in the balance. They remain in ninth, outside of the automatic qualification spots for the Round of 16.
This festive period was always going to be make or break for Postecoglou and Spurs' short-term future. They are in the middle of a crucial run of nine games in 30 days -- it's a sequence of fixtures that Postecoglou admitted in November would prove "pivotal" for his team.
"At the end of that period, we could be in a decent position for a strong second half of the year, so for us, it is an important period," Postecoglou said the day before the dramatic 4-0 win over Manchester City that started the nine-game run.
"You know there are no more international breaks, so the full focus is here, so you can build some momentum through that, or if things don't go well, you could get yourself into a bit of a grind. So, for us, it's going to be a really pivotal part of the season."
Six games into that nine-game run, there certainly has been plenty of grind.
Without Dejan Kulusevski and Dominic Solanke, who were named on the bench, Spurs carried little attacking threat in the first half.
The home side were the aggressors, snapping into tackles that brought screams of support from the relentless home crowd. Nedim Bajrami came closest to opening the scoring with a fierce effort that Fraser Forster tipped over the crossbar. The best Spurs opening came from a Rodrigo Bentancur cross that whistled through a Solanke-shaped hole on the edge of the six-yard box.
The second period brought Kulusevski's introduction, in place of the often-haphazard Timo Werner, whose performance Postecoglou later described as "unacceptable." Two minutes after the restart, though, Rangers took the lead after Hamza Igamane lashed in James Tavernier's cross.
Now, the Rangers fans had the moment they had been waiting for. They bounced, screamed and revelled in Postecoglou's misfortune. As soon as they had refilled their lungs, the home fans bellowed in unison: "You're getting sacked in the morning."
More chances for Rangers came and went, first Václav Černý wriggled through the Spurs but couldn't get his shot away, then Mohamed Diomande's deflected effort had Forster scrambling as the ball whistled past the post.
Four minutes later, Postecoglou had made three changes; on came Lucas Bergvall, Solanke and Pape Matar Sarr for Bentancur, Brennan Johnson and Yves Bissouma.
It proved the correct intervention at just the right time for Postecoglou to salvage the game, and maybe his job. Solanke and Kulusevski combined in the 75th minute to open enough space on the edge of the penalty area before the Sweden international rolled a low shot past Jack Butland.
Bergvall has been criticised for the impact he has made in games since signing for Spurs in the summer, but the 18-year-old added the bite and guile the Spurs' midfield had been missing from the Bissouma-Bentancur axis.
Before their late turnaround, Postecoglou's assertion that he "wins things in his second year" certainly appeared misplaced. In truth, his teams have struggled in Europe.
Despite their domestic successes, his Celtic team never made it out of a UEFA Champions League or Europa League group or won a knockout-round game after dropping down into the UEFA Conference League playoffs.
The maelstrom of Thursday to Sunday games is perhaps too much for Postecoglou's high-energy philosophy. No team in the Premier League has pressed so high or made more off-the-ball sprints as Spurs this season, and Postecoglou's "never stop" ethos has had unintended consequences. He was unable to call upon eight first-team players for Thursday night's game, with five of them nursing muscular issues, including first-choice defensive pair Cristian Romero and Micky van de Ven.
His lack of options prompted Postecoglou to name 18-year-old Archie Gray in the centre of the Spurs' defence. Like his manager, Gray also has links to Scotland -- his father, Andy, grandfather Frank (European Cup winner with Nottingham Forest and Leeds United legend) and great uncle Eddie (legendary former Leeds player and manager) all represented Scotland -- Frank and Eddie were born in Glasgow, around seven miles from Ibrox.