"It's a good job there was video in this case", Griezmann told beIN Sport TV.
Just four minutes later, however, France's Samuel Umtiti made a weird mistake, his flailing arm making contact with a high cross from Aaron Mooy, forcing the referee to award another penalty, which Australian captain Mile Jedinak converted.
Australia's players claim they are ready to "move on" and are focusing on trying to beat Denmark on Thursday (Jun 21) in a bid to reignite their bid for a place in the last 16.
GK Mat Ryan, 6 - Beaten by a Griezmann penalty and an unlucky deflection off Paul Pogba, but otherwise a solid performance.
Mile Jedinak quickly drew the Socceroos level with a penalty at the other end following Samuel Umtiti's inexplicable handball, before goal-line technology was required for France's late victor, claimed by Paul Pogba after a hefty deflection off Aziz Behich.
France went into this tournament as one of the favourites to lift the World Cup trophy, but they have much to do if they hope to go far in this tournament. It was complicated, the Australian team was very good. "We can and we will", declared the France boss. There were many situations in which France did not know what to do anymore. "So that's a big compliment for us".
Minutes later Australia drew level through a spot-kick of their own although it was awarded by the referee, with Mile Jedinak coolly beating Hugo Lloris.
Deschamps, a World Cup victor with France in 1998, will be thanking his lucky stars after a performance which poses more questions than answers about his ambitious side, the second-youngest in the tournament after Nigeria.
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His fellow superstar Messi, with whom he has monopolised the world player of the year award for a decade, is under enormous pressure to secure his first major global trophy and make amends for Argentina's painful loss to Germany in the 2014 final.
It was French keeper Hugo Lloris who was tested most, keeping out a Mooy free kick that French defender Corentin Tolisso nearly deflected into the bottom corner of his own goal.
The way Van Marwijk set up his defence gave little space for Le Bleus to exploit and any through or long balls were either dealt with by the defence or went through to Matt Ryan in goal.
The World Cup Ball designed this year, known as the Telstar 18, was supposed to be tough and durable. Griezmann converted the resulting penalty, firing to the right corner.
Paul Pogba celebrates after scoring the second for France.
Australia delivered a gritty display that bodes well for its next two matches.
But Australia spent most of the first half defending and ultimately frustrating France, rarely creating real chances of their own.
The star striker went down easily and despite officials waving the penalty it was ultimately awarded by the VAR.