Federation Internationale de Football Association director of referees Massimo Busacca admits the system has been rushed in for the World Cup, but insists officials are ready and that VAR will help referees make better decisions in Russia.
A yellow card for the Socceroos defender and a penalty followed, with Griezmann expertly dispatching that into the corner to give France the lead.
"I hoped that maybe one time there would be a very honest referee, and in that moment, that he wouldn't go to the video screen", the Dutchman said.
While Australia failed to convert the free-kick which was awarded to them after 75th minute of the match, France-who replaced Griezmann with Olivier Giroud- were searching for opportunities with no avail.
France have been widely tipped to win the group by most, and deservedly so, while Australia are fancied by most to finish beneath fellow group rivals Peru and Denmark.
But a shot by Frenchman Paul Pogba in the 81st minute took a deflection off Aziz Behich and bounced off the cross bar over the line, giving the French the winning goal.
France coach Didier Deschamps said on Sunday his key forward Antoine Griezmann "must do more", after a disappointing performance in their opening 2-1 World Cup win against Australia.
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When new Australia coach Van Marwijk guided Netherlands to the World Cup final in 2010, he did so not by playing handsome football throughout the competition - they were a team with plenty of bite and aggression in their ranks. No one expected we could play like this against France.
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.
On 17 minutes France 'keeper Hugo Lloris turned a risky deflection from Corentin Tolisso around his far post.
France's early verve was sorely lacking for the remainder of the half, with Australia able to keep their more illustrious opponents comfortably at arm's length before the interval.
Griezmann stepped up and confidently opened Les Bleus' World Cup account in the 58th minute.
The real drama, however, unfolded after the interval with the VAR decision.