Argentine boss Lionel Scaloni had said before the game he did not want the fixture to become about the conflict over the British overseas territory.
But after his side came from 1-0 down with five minutes left on Wednesday (Thursday AEST) to win 2-1 and reach a second successive World Cup final, players held up a banner that read 'Las Malvinas son Argentinas' which translates to 'The Falkland Islands are Argentinian'.
The banner had also been visible in the stands.
One of those players involved was midfielder and unused substitute Giovani Lo Celso, who previously played in England for Tottenham Hostpur.
World football body FIFA bans players and officials from displaying political messages around World Cup matches so the defending South American and world champions could therefore face sanctions.
Political tensions linger between Argentina and Great Britain over the Falkland Islands, which boiled over into conflict in 1982.
Argentina has repeatedly claimed sovereignty over the Falkland Islands, which are about 8000 miles (12,875km) from Britain and 300 miles (483km) from mainland Argentina.
Argentinian Vice President Victoria Villarruel wrote on X before the game: "We play against the usurping pirates.
"I'm not going to be politically correct or cold-hearted; against the English, it's always something more."
And she tweeted a victory message at fulltime saying, "it wasn't just another match" alongside a video of what appeared to be Argentinian soldiers.
Villarruel's father fought in the Falklands War for Argentina's military dictatorship.
With DPA.
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