Fernandez was sent off for a second booking after clattering into Spain's Pau Cubarsi in the closing stages of normal time in Sunday's 1-0 loss.
The 25-year-old Chelsea midfielder's premature exit was the latest in a series of clashes that cast a shadow over Argentina's run to the final.
Leandro Paredes appeared to throw punches at members of the Spain squad as they celebrated their victory, with FIFA subsequently launching an investigation into potential disciplinary breaches following the unsavoury post-match scenes.
They also turned their backs on Spain when the Spanish received their medals and the trophy.
Argentina's players also caused controversy by displaying a banner reading "Las Malvinas son Argentinas" (The Falklands are Argentine) after beating England in the semi-finals.
Argentina invaded the British Overseas Territory in the South Atlantic in 1982.
But Britain regained the archipelago in a brief war after then prime minister Margaret Thatcher dispatched a naval task force.
Fernandez took to Instagram to defend his country's World Cup performance, but made no mention of his sending-off in his message to supporters.
"As time goes by, you realise there is something much bigger than just a result," he said.
"For years, this group has represented the team in the best possible way. It teaches that competing isn't just about winning; it's about giving your all for the jersey and never giving up."
Fernandez was a member of the Argentina team that beat France to win the 2022 World Cup in Qatar.
But Fernandez's hopes of a second successive title were shattered after his dismissal as Ferran Torres's 106th-minute strike settled a dour final marred by Argentina's defensive tactics.
"It has been a privilege to be part of a group that always stepped up, competed at the highest level, and defended these colours with pride, humility, and commitment," he said.
"I want to thank all the Argentina fans. Thank you for always being there, for supporting us in every match, for the affection, for the unconditional support, and for making us feel at home anywhere in the world.
"Wearing my country's jersey is the greatest honour of my career, and I will continue to give my all every time I get to defend it."