The German had been bullish about speculation of his future but seemed accepting that his position was in serious threat at the post-match media conference.
"It's not my call anyway. I don't know how people will react in our organisation,'' Osieck said, likely only a matter of moments before he was dismissed.
Gallop brushed Australian media shortly after the game in Paris in a strong indication the sacking was imminent.
The defeat to the 25th-ranked France was labelled a disgrace by former Socceroos, with Mark Bosnich calling for Osieck's immediate resignation.
Fellow Fox Sports pundit Robbie Slater declared: ``We have never been embarrassed like this before.''
A France side brimming with superstars - led by the brilliant Franck Ribery - were ruthless against an Australian outfit that again looked disjointed and wasteful with any possession.
Reigning European player of the year Ribery was involved in most goals, in-form Arsenal striker Olivier Giroud scored twice in the first half while Real Madrid star Karim Benzema came off the bench to end his 16-month international goal drought.
Australia have conceded 19 goals in their past four matches and a new coach will have only eight months to turn things around for Brazil.
Former coach Guus Hiddink has been mentioned as a potential replacement, while there have also been calls for a local coach such as Ange Postecoglou or Graham Arnold to be installed.
Former Liverpool boss Gerard Houllier - who was at the match in Paris - has also been linked with the role as he has been in the past.
Assistant coach Aurelio Vidmar will likely take the reins for Tuesday's clash with Canada in London.
While Osieck had been dealt several injury blows leading into the match at Parc des Princes, Tim Cahill and Luke Wilkshire returned after missing the Brazil loss.
Mitch Langerak, 25, was handed a debut in goals and David Carney was back after more than a year out at left back.
James Holland was a surprise choice at right back while Rhys Williams partnered captain Lucas Neill in central defence.
But it was night to forget for every Australian player.
Carney had a particularly disastrous first half and was substituted at the break for youngster Jason Davidson.
After Langerak had made a brilliant save to deny Giroud early, there was a touch of fortune as the hosts opened the scoring in the eighth minute through a Ribery penalty.
Carney was harshly adjudged to have hand-balled in the box, though his decision to raise his arms while defending a cross was bizarre.
Giroud added a second for France in the 16th minute with a deft first-time chip over Langerak following some good work from Ribery.
The in-form Arsenal striker had his double in the 27th minute and Ribery was again involved, combining beautifully with Manchester City star Samir Nasri who provided the last pass.
France were scoring for fun and midfielder Yohan Cabaye was able to get in on the act, blasting a long-range shot through Carney's legs and beyond Langerak.
France started the second half as they did the match, and the goals continued to flow.
Mathieu Debuchy scored in the 47th minute with a brilliant first-time finish following another failed Socceroos clearance.
It was 6-0 only two minutes later when substitute Benzema ended his baron run following some more splendid build-up by Ribery.
Australia had their first shot of the game in the 60th minute when Cahill fired over the bar from outside the box and they at least ensured the last half hour of Osieck's reign was goalless.
-AAP
