Messi finally posted a statement on his facebook account late Monday having hidden his devastation at losing another major final since the 4-1 penalty shootout defeat by Chile on Saturday.
"There's nothing more painful in football than losing a final," Messi said.
"But I don't want to leave it any longer to say thank you to everyone who has always supported us and continued to during the tough moments."
Messi, 28, has now lost one World Cup and two Copa America finals and still has to win a major international event despite his success with Barcelona.
Argentina, beaten 1-0 by Germany in last year's World Cup final, have now not won a major title for 22 years.
Messi left the pitch ashen faced after the latest defeat and unconfirmed Spanish media reports said he turned down the player of the tournament trophy. The trophy was withdrawn before the presentation ceremony in Santiago.
Messi and the other Argentine stars were criticised by the country's media for their performance. Members of his family were also abused by Chilean fans at the match, according to Argentinian media.
Some observers have warned that Messi could walk away from the national side.
"One day this boy is going to get tired and will not want to come to play for the team," former Argentine international Matias Almeyda, now coach of the Banfield club, told Fox Sports television.
"He's the best player in the world and he is not treated in the way he deserves," Almeyda added.
Messi had a brilliant season with the all-conquering Barcelona but Almeyda said "it is very difficult (for Argentine players) to repeat for the national team what they do for their clubs.
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