The Argentines had Enzo Fernandez sent off in second-half stoppage time, which left them with a mountain to climb.
Argentina great Lionel Messi left the pitch in tears after playing in his third World Cup final, a feat only previously achieved by Brazilian Cafu.
Scaloni said he had not spoken to Messi about his future but thought his tournament, during which he played every minute of every knockout match and scored eight goals, was “unbelievable”.
“He’s 39 years old now,” Scaloni said. “It was crystal clear for me that he was going to play up until he decided not to.
“I hope that everyone feels proud of him, of what he’s achieved, because he’s the best football player ever to set foot on a pitch. I have no doubt about this, and what he did during this World Cup was incredible. But also what he did before this.”
Messi won everything at club level before leading his country to a World Cup triumph in 2022 and Copa America titles in 2021 and 2024.
Scaloni was reduced to tears as he discussed his own future.
“I will talk to the president (of the football federation),” said the 48-year-old. “I believe it’s only fair that I can take this time for myself to think this through. I never thought I would get to this place and it’s wonderful.
“In order to continue, you need a great deal of things, resetting your mind, rebooting, creating a group like this again – that is very difficult.
“I am very sorry,” he said as the emotions finally overwhelmed him and he left the press conference room.