The Lilywhites reinforced their backline with two new central additions over the summer, bringing in Micky van de Ven and Ashley Phillips from Wolfsburg and Blackburn Rovers respectively.
The duo arrived in North London in the wake of Japhet Tanganga and Joe Rodon's loan departures to Augsburg and Leeds United respectively, while Davinson Sanchez left for Galatasaray on a permanent deal.
As Postecoglou switched to a four-man backline, Van de Ven seamlessly slotted into the Australian's system alongside Cristian Romero, and their partnership was integral to Spurs' record-breaking start to the season.
With Van de Ven and Romero shielding Guglielmo Vicario, Postecoglou witnessed his side glean 26 points from the first 30 on offer in the 2023-24 season, the best record of any Premier League manager from their first 10 games in the competition.
However, Van de Ven then suffered a serious hamstring problem during November's defeat to Chelsea, where Romero was also sent off, and the Dutchman is expected to spend another few weeks on the sidelines.
Van de Ven's injury and Romero's suspension exposed Tottenham's lack of depth in the heart of defence, where Eric Dier and Phillips are Postecoglou's only alternative options, and the duo are also in the treatment room with groin and ankle injuries respectively.
As a result, left-back Ben Davies has often been forced to fill in alongside Romero, while Emerson Royal and Pierre-Emile Hojbjerg have also been deployed as emergency centre-backs, and Van de Ven's absence has coincided with Tottenham's winter collapse.
Including the 4-1 loss to Chelsea in which Van de Ven sustained his injury, Tottenham took just one point from five top-flight matches and made unwanted history as the first team to take the lead in five successive Premier League contests but not win any of them.
The Lilywhites pulled themselves out of that rut by defeating Newcastle United 4-1 last weekend, though, and the fifth-placed North London giants can draw level on points with Manchester City should they overcome Nottingham Forest on Friday.
Speaking to the media at his pre-game press conference, as quoted by football.london, Postecoglou waxed lyrical about Davies's "outstanding" performances in the heart of the backline but stressed the need to sign another defender next month, when Dier will enter the final six months of his contract.
"I thought Ben Davies was outstanding. He's done remarkably well. He's getting a run of games. We've got to be mindful he's not a centre-back and he's growing into that role," Postecoglou said.
"Ben is still adapting to it. He's done remarkably well. Centre-back is still a position, especially in our structure, where you need outstanding attributes and we've been very fortunate to have him that he's been able to adapt there. He's great at taking on information.
"He's been helped by having Romero back and Vic has taken on a leadership role back there as well. We need to sign another centre-back though because at the moment we're on tenterhooks in case something else happens there."
A wide array of centre-backs have been linked with January moves to Tottenham, including Bournemouth duo Lloyd Kelly and Ilya Zabarnyi, the former of whom is due to become a free agent at the end of the season.
Everton pair Ben Godfrey and Jarrad Branthwaite are also said to be on Spurs' radar, as are Atalanta BC's Giorgio Scalvini and Crystal Palace's Marc Guehi, but Tottenham could be priced out of a move for the latter.
Postecoglou also revealed a fresh injury blow for his squad ahead of the trip to the City Ground, as Giovani Lo Celso will sit out the clash with Steve Cooper's side.