Captain Hugo Lloris' form has suffered for France recently, but the Tottenham goalkeeper was alert to keep Australia at bay in the first half.
Under the VAR regulations, replays can only be used to assist referees in the case of a "clear and obvious error" rather than assisting officials to make correct decisions for matters of interpretation.
The VAR system is making its first appearance at a World Cup.
Even Pogba's goal might not have stood in the days before technology was brought into the game with the midfielder's shot looping off the shin of Aziz Behich, hitting the crossbar and bouncing down inside the goal before coming back out.
Samuel Umtiti was involved in one of the most weird moments at the World Cup so far in France's match against Australia.More news: How Suns Plan To Probe Kawhi Leonard Trade With Spurs
Pogba, whose victor was aided by goal-line technology after his strike clipped a defender and bounced off the underside of the bar, told TF1: "It is the World Cup - there are no small teams".
'I don't feel like we were beaten by a better team, nearly by technology, ' goalkeeper Mat Ryan said.
"I was pretty confident, to be fair", Josh Risdon said about the call that went against him.
"The majority of French players were too comfortable or not wanting to risk too much, or not confident enough to make things happen". They're a proud side who play with passion, and I've been told there's 30,000 Peruvians in Moscow. "Our opponents always play deep against us and we need to find a way to play better in those kind of matches".
France opened up its 2018 FIFA World Cup campaign in Group C with a win, but it didn't look sharp in doing so.
"It was a hard match, it was complicated and the Australian team were very good".