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Published 07:22 27 Jun 2016 BST
Updated 07:24 27 Jun 2016 BST
The defeat also means Argentina have lost three finals in the last three summers, and their captain appears to have had enough.
"For me the national team is over. I've done all I can, it hurts not to be a champion," Messi said.
"It's been four finals, it's not meant for me. I tried. It was the thing I wanted the most, but I couldn't get it, so I think it's over."Messi was also part of the Argentina team that lost to Brazil in the 2007 Copa America final. Here's his miss from Sunday's final, which looks to be his final kick in an Argentina jersey.
