The 21-year-old made the breakthrough for his side 11 minutes from time in Brasilia, as France booked their place in the quarter-finals with a 2-0 victory.
"I knew there was a whole country that would support us - scoring that goal has freed us," Pogba told TF1. "I am very happy for the team and for the whole of France.
"Playing in the last eight of the World Cup has always been a dream of mine. This is one of the proudest moments of my life."
France will face the winner of tonight's Algeria-Germany clash, live commentary of which can be found here.