Postecoglou drew immediate praise for bringing fast-paced, attacking football back to North London following the failed stints of Jose Mourinho, Antonio Conte and Nuno Espirito Santo, none of whom lasted 24 months in the hotseat.
However, Tottenham remain without a single piece of silverware since the 2007-08 EFL Cup and are currently languishing in 10th place in the Premier League table, five points off the Champions League spots with 16 games gone.
Next up for the Lilywhites are two huge fixtures against Manchester United in the EFL Cup quarter-finals and Liverpool at home in the Premier League, but Keller does not believe that Postecoglou could be given the boot if Spurs disappoint in both fixtures.
"I wouldn't say it's make or break," Keller told Sports Mole. "I think you can see what Ange is looking to achieve at Tottenham, and with the 4-0 win over Man City when Spurs perform like that then there is optimism for the future."
Keller sends Postecoglou message to Daniel Levy as Spurs' "inconsistency" assessed
Postecoglou is the fourth permanent head coach that Tottenham have had since the start of the 2019-20 campaign, a spell which also includes Ryan Mason's two spells as interim boss and Cristian Stellini's extremely ill-fated reign after Conte departed.
All of Santo, Mourinho and Conte failed in their quest to end Tottenham's trophy hoodoo, but Postecoglou's team are still fighting on four fronts this season, also battling for glory in the Europa League and FA Cup.
Following September's 1-0 North London derby loss to rivals Arsenal, Postecoglou cut an extremely defiant figure and insisted that he "always wins things" in his second year in the job - a statement that is backed up by his managerial history.
Even though the former Celtic boss is yet to oversee a total transformation in North London, Keller - who played 97 times for Tottenham between 2001 and 2005 - believes that injuries and money have played a part in Spurs' inconsistency this term.
"You can't keep changing managers," Keller said. "You look at Spurs and they have had injuries, but there has been lots of inconsistency this season which must improve if they are going to challenge for European positions.
"But you look at the squad and the players and then look at other teams in the top four who have spent a lot more than Spurs. Ange must be given time to build the team he wants."
Have Tottenham spent less than the top-four teams?
There is the perpetual perception that Levy refuses to open his war-chest while the likes of Manchester City, Arsenal and Chelsea splash the cash freely - which was brought up again recently by Spurs defender Cristian Romero - but that was not strictly true in the summer transfer window just gone.
Indeed, Tottenham spent a total of £128.4m on four arrivals - Lucas Bergvall, Wilson Odobert, Archie Gray and Dominic Solanke - and only one of the current top-four teams recorded a higher outlay in the last market.
That team was unsurprisingly Chelsea, whose total spending in the summer exceeded £200m, but Arsenal, Liverpool and surprise package Nottingham Forest all kept their totals under £100m.
David Raya, Riccardo Calafiori and Mikel Merino set Arsenal back by £91.7m, while Forest were just under at £90.8m, and Liverpool only forked out £35.3m on Giorgi Mamardashvili and Federico Chiesa.
Kasey Keller was speaking to Sports Mole on behalf of William Hill Vegas.
Written by
Ben Knapton