Referee Nestor Pitana was alerted to a possible handball and after checking the off-field screen he decided Ivan Perisic had handled the ball in trying to clear a France set-piece.
The match at the Luzhniki Stadium had already seen the first own goal in a FIFA World Cup final when the ball flicked off Croatia striker Mario Manduzkic and past his own goalkeeper to put France 1-0 up after 18 minutes.
FIFA have declared the use of VAR at the World Cup in Russia a success.
France went on to win the game 4-2 to claim the FIFA World Cup.
