Griezmann admitted that pressure surrounding the French team, with seven players out of the 11 starters having never played in a World Cup before, was intense.
After reviewing the footage pitchside for little more than 30 seconds, Cunha overturned his original decision and awarded France a penalty, much to the fury of the Australian players.
The French can thank technology for providing them a "fair" 2-1 win over Australia.
Griezmann hit a powerful shot that left Ryan stranded, four minutes before Jedinak then sent France goalkeeper Hugo Lloris the wrong way to put the teams level following Umtiti's clumsy foul. A first in World Cup history.
The Uruguayan official Andrés Cunha reversed his original reaction that Josh Risdon's challenge on Antoine Griezmann was not worthy of a penalty, after being guided to check the incident by the video assistant referee Mauro Vigliano.
Van Marwijk, who led the Netherlands to the final in 2010 before an extra-time defeat to Spain, said however he was not bitter against France.
But after 15 minutes of solid defending, Australia grew into the game and conjured up the best chance so far.
"It's true that he went through a bad patch following the competition but he showed how [much of] an incredible player he was and he is by scoring goal after goal".
"It's also a human being so everybody makes mistakes".
The 65-year-old Dutchman added: "It's very hard to decide when you have 50,000 people (in the stadium) on his back, he must decide".
Didier Deschamps' Les Bleus head to Russian Federation among the favourites to triumph on July 14 but will remember all too well their group stage exits in 2002, as defending champions, and 2010.
"From my position I could not see it [the penalty] really well but at first I thought it was no penalty".
But France pinched the points in the 81st minute with what Van Marwijk described as "such a lucky goal". It was confirmed by goal line technology.
"I don't feel like we were beaten by a better team, nearly by technology", goalkeeper Mat Ryan said.
The Socceroos, rank outsiders, outplayed tournament fancies France for much of the contest.
"There were a lot of moments they didn't know what to do anymore". I'm proud but disappointed. "No one expected we could play like this against France", he said.
"I wish them all the luck, and I mean that", he said.