Long-serving goalkeeper Mark Bosnich and English Premier League winner Robbie Slater have laid into Postecoglou after Australia's qualifying fate was revealed.
Australia defeated Thailand 2-1 in Melbourne on Tuesday night, which allowed Saudi Arabia to leapfrog the Socceroos into a World Cup place by beating Japan 1-0 in Jeddah on Wednesday morning (AEST).
The Socceroos must now confront a dangerous two-pronged play-off route, which begins with a home and away leg with Syria next month.
According to Bosnich and Slater, they should also confront a coaching change.
The former Aston Villa and Manchester United gloveman laid bare his issues with Postecoglou's approach on Tuesday, starting with his divisive 3-2-4-1 formation.
"Don't be using the national team as an experimental laboratory. It's not there for that. It's too important for that," Bosnich told Fox Sports.
"We're not England or Brazil or federations with a lot of money. We are strapped for cash and this game in this country needs us to qualify for the World Cup all the time.
"At the moment, he's hanging by a thread in my opinion.
"If we go through the play-off route there should be serious consideration given to the fact we need a different voice because those players, regardless of what they're saying publicly, aren't responding like they used to."
Slater saved his opinions until Wednesday morning, when he said it was "time for a change".
The two-time Oceania player of the year didn't directly call for Postecoglou's head but did criticise the insular nature of his set-up on Twitter.
"We need a new approach! Socceroos have lost there (sic) way! Enough bullshit! We now need saving," he wrote.
"Sick of this blind alley culture where you can't ask a question as it's an insult to suggest there is a problem!
"To be fair it's a mess and the players think we are against them! Who told them that I wonder! Toxic crap for me!"