Martinez was a one-man barrier to wave after wave of Spain attempts on goal at the MetLife Stadium before Ferran Torres finally fired the winner past him in extra time.
The veteran goal keeper was in tears at full-time as Argentina prepared to wave goodbye to talismanic captain Lionel Messi.
39-year-old Messi will not play at the 2030 World Cup. but he's yet to confirm his immediate plans for Argentina, and Martinez is in a similar situation.
"I dreamt we'd win it again, I dreamt of bringing it back to Argentina and making history once more," Martinez wrote in a post on Instagram.
"The truth is, the pain is hard to explain. There are many things to reflect on and how to move forward, and if it's time to step aside.
"I'm so sorry, I truly tried my best to help my country and my team-mates."
Martinez has been first choice for Argentina under Lionel Scaloni - who could also resign at the end of 2026 - with the Aston Villa stopper winning the 2022 World Cup alongside two Copa Americas across his 67 caps.
The 33-year-old is expected to speak with Villa boss Unai Emery before making a decision, ahead of a return to the UEFA Champions League at club level this season, with Argentina yet to confirm their match plans for the rest of the year.