The Socceroos, playing their 500th international match, were expected to make amends for their dour 0-0 draw with the United Arab Emirates on Saturday morning.
And although it was a more entertaining contest at Doha's Abdullah bin Nasser bin Khalifa Stadium, the men in green and gold again proved unable to breach the opposition's defence, conceding a soft goal to return from two Gulf friendlies empty-handed.
Postecoglou made eight changes to the starting XI that were held by the UAE, centre-back Alex Wilkinson, captain Mile Jedinak and forward Robbie Kruse the only survivors.
Mitch Langerak took the gloves from Mat Ryan, as Chris Herd, Nikolai Topor-Stanley and Aziz Behich joined Wilkinson at the back.
Mark Bresciano was deployed slightly ahead of holder Jedinak, with Tommy Oar on the left, James Troisi at No.10 and Tim Cahill up front.
It took just two minutes for some familiar faces to resume their well-established partnership. Bresciano picked out Cahill unmarked at the back post, only for the New York Red Bulls man to power an uncharacteristically weak effort harmlessly into the turf.
Despite dominating possession, the Socceroos had to wait until the 24th minute for another presentable chance to arrive. This time Cahill, winning an aerial challenge inside the area, nodded down to Troisi, who saw the angle for a right-foot curler closed off, before his eventual left-foot strike was well saved by goalkeeper Qasem Burhan.
Reading's Adam Federici replaced Langerak at half-time, while Josh Brillante came on for Jedinak. Australia stepped things up early in the second half, although a succession of corners and half-chances failed to really trouble the hosts.
And they were punished for not making more of those opportunities. Khalfan sprang the offside trap to slot a low finish beyond Federici in the 61st minute, Topor-Stanley having narrowly failed to cut out Sebastian Soria's assist.
Cahill had a decent chance to level in the 68th minute, turning his man just inside the area before firing a low strike straight at Qasem.
Postecoglou progressively introduced Bernie Ibini, Mathew Leckie, Brad Smith and Ivan Franjic for Kruse, Cahill, Oar and Herd respectively from the hour-mark onwards. But the men in green and gold struggled to recapture the momentum they had built early in the second period, the hosts seeing out the time remaining in relative comfortable to claim the scalp of a regional powerhouse.
Teams
Qatar:
Qasem Burhan, Ibrahim Majid, Mohammed Musa (Ismaeel Mohammad 67'), Abdulaziz Hatem, Almahdi Ali, Abdelkarim Hassan, Wesam Rizik (Khaled Al Zereiqi 65'), Khalfan Ibrahim, Ahmed Abdul Maqsoud (Luiz Ceara 65'), Hassan Khalid, Sebastian Soria (Meshaal Abdulla 73').
Australia:
Mitch Langerak (gk) (Adam Federici 46'), Tim Cahill, Nikolai Topor-Stanley, James Troisi, Robbie Kruse (Bernie Ibini 63'), Tommy Oar, Aziz Behich, Chris Herd (Ivan Franjic 63'), Mile Jedinak (Josh Brillante 46'), Alex Wilkinson, Mark Bresciano
Scorer: Khalfan Ibrahim 61'
Venue: Abdullah bin Nasser bin Khalifa Stadium