Several members of Lionel Scaloni's side held up flag referencing the Falklands Islands as part of their post-match celebrations at the Atlanta Stadium.
Midfielder Giovani Lo Celso brought onto the pitch a banner saying, “Las Malvinas son Argentinas,” which translates to “The Malvinas are Argentine.”
Premier League pair Cristian Romero and Lisandro Martinez, who both play in England for Tottenham and Man United respectively, were among the players holding the banner.
It's not first time Argentina's squad have displayed such a symbol. In 2014, FIFA fined the Argentina FA £20,000 after players displayed a banner in support of their country's claims to the islands.
That fine and punishment was not implemented until after their participation in the World Cup and a similar pattern is expected to follow here.
Calls from the UK Government for FIFA to look into the matter and hand out suspensions have come in force, but Argentina star Leandro Paredes backed the team's stance.
"Sadly, it's a sad part of our history - for everyone involved in that chapter of, I repeat, our history. And it hurts.
"We played for them, too. For all the people, for our entire nation. I believe we did it in the best possible way."
FIFA are expected to offer an update on the situation before the final with Martinez, Romero and Lo Celso facing potential future punishments.