A video posted by Argentina international Enzo Fernandez on Instagram after his team beat Colombia 1-0 in Sunday's final, featured a song sung by some members of the Argentina squad about France's players of African descent.
FIFA is investigating the video after French Football Federation (FFF) said it was "racist and discriminatory". Chelsea, the Premier League club Fernandez plays for, have also started an internal disciplinary procedure over the matter.
Fernandez later apologised for the video saying he got caught up in the euphoria of celebrations and the song does not reflect his beliefs or character as he stands against discrimination.
"It doesn't matter if you are in a moment of euphoria because you have won an important trophy," Lloris told the BBC on Thursday. "It demands even more responsibility when you are a winner."
"We all stand against discrimination and racism. I just think and hope it is a mistake. We all make mistakes sometimes and hopefully they will learn from it."
Argentina's Vice President Victoria Villarruel defended Fernandez and the team and the country's undersecretary for sports, Julio Garro, was removed from his position for suggesting that captain Lionel Messi apologise for the chants.
Lloris, who is France's most capped player and their 2018 World Cup winning captain, said Argentina deserved credit for what they have achieved in the sport in the last few years having become "the face of football in the world".
"You (Argentinian players) are an example for others, especially the kids. It was a proper attack about the French people, especially for the French people who have some African origin and family," he said.
