Antoine Griezmann went down after a tackle in the penalty box in the second half of the Group C fixture.
Uruguayan referee Andres Cunha did not award a penalty but after viewing the VAR footage, ruled it was a spot-kick and Griezmann gave France a 1-0 lead.
Socceroos skipper Mile Jedinak sent his French counterpart Hugo Lloris the wrong way to give Australia hopes of forcing a draw at the Kazan Arena but Pogba grabbed the victor in the 81st minute. "He caught me on the left foot".
"But, like I said, we have still got to play the game and focus on the game and try not to let those little things, or sometimes they could be big things, try not to let it distract us to much".
The VAR almost came into play within minutes of that opening goal, when Samuel Umtiti left his arm up in the air so that the ball would hit his hand, but, this time Cunha, after taking a couple of seconds, awarded Australia the penalty, without the need of technology.
France face Peru in their next match and will be buoyed by the three-point start, with many predicting the team can go a long way in Russian Federation.
He said: "I'm not going to complain about VAR because it was in our favour obviously". No one expected we could play like this against France.
"You always knew that they are a threat all over the pitch, so it was just about keeping that concentration".
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The Prime Minister also said that it is "a shame" to hear that the trump justifies their rates as a problem of national security.
Yet the 33-year-old was uncertain whether he would even feature in Australia's World Cup opener until a few hours before the match.
Deschamps started with a three-man attack comprising of Ousmane Dembele, Kylian Mbappe and Griezmann with Pogba and Corentin Tolisso operating on either side of N'Golo Kante in the midfield.
Didier Deschamps' side needed just six minutes to test Mathew Ryan in the Australia goal. Midfielder Aaron Mooy swung in a risky free-kick which took a nick off Corentin Tolisso and nearly crept into the bottom corner for an own goal.
To muscle up his team for the next game against Peru in Group C, Deschamps may be tempted to include Matuidi in his starting lineup, and revert to a 4-4-2 formation with Giroud and Griezmann up front. The Atletico Madrid forward struck the ball into the right corner to open the scoring.
As for the 2-1 loss, Jedinak said the players were shattered not to have hung on for a draw.
Australia then spent most of the first half defending and ultimately frustrating France, rarely creating real chances of their own.
The real drama, however, unfolded after the interval with the VAR decision.