The 59-year-old and his players were booed after the full-time whistle at the Tottenham Hotspur Stadium, with fans lamenting the lack of consistency that has plagued the team since the Australian's appointment in June 2023.
Spurs had beaten both champions Manchester City 2-1 on October 30 in the EFL Cup and Aston Villa 4-1 in their following match on November 3, but in the past week they lost 3-2 in the Europa League against Galatasaray and 2-1 against Ipswich.
Postecoglou's side are now 10th in the Premier League with 16 points after 11 matchweeks, but are only in the top half of table thanks to having better goal difference than Brentford.
However, Football Insider report that the manager has plenty of credit in the bank and has the support of officials at the club as he tries to drive Tottenham up the table.
Defensive concerns
Spurs' defeat against Ipswich was their fifth of the Premier League season and was also the second time they had lost against a winless opponent having been beaten 1-0 by Crystal Palace in late October.
One area of concern in regard to Tottenham in recent seasons has been their defensive frailty, with the club having five clean sheets in their last 40 top-flight matches.
The Australian has also come in for criticism after his comments in the aftermath of his side's 1-0 loss against rivals Arsenal in September, saying that he always wins trophies in his second season in charge.
"I'll correct myself - I don't usually win things, I always win things in my second year. Nothing's changed," he told reporters in the after the North London derby defeat when asked if he stood by his claims.
While his claims highlighted his immense self-belief, some found his remarks to be off-putting considering Spurs have not won a trophy since beating Chelsea in the EFL Cup final in 2008 and other managers such as the legendary Jose Mourinho have failed to bring silverware to the club.
If he were to be sacked, Postecoglou would become the fifth manager to have been dismissed from the Tottenham bench in the last five years, but the list of potential replacements looks increasingly thin given the likes of Ruben Amorim and Thomas Tuchel are off the table.
Young and promising squad
Perhaps the Australian deserves some leniency for his side's inconsistencies, especially as he has built a remarkably promising young squad that would naturally experience peaks and troughs over the course of their development.
Indeed, many of his core players such as Dejan Kulusevski, Micky van de Ven and Destiny Udogie are 24 years old or younger.
Summer signing Archie Gray is regarded by some as possessing immense potential, but he is only set to celebrate his 19th birthday in March 2025.
Additionally, despite the youth and inexperience in his squad, Postecoglou has already managed to produce a formidable attacking side, with the team top of the Premier League's goalscoring charts having netted 23 times this campaign.
There is no doubt that Spurs will need to fix address their defensive issues, either on the training ground or in the transfer market, but the 2024-25 season still has a long way to go and they are only three points from fourth-placed Arsenal as well as third-placed Chelsea.