The South American giants were favoured to win the competition, in which they acted as hosting country, but were ousted in the quarter-finals by eventual champions Uruguay in a penalty shootout.
The diminutive striker admitted that Argentina's performances did not match the team's expectations, but indicated that the only thing to do is to move on.
"I am hurt.... It did not go as we expected, but now we have to look forward," Messi said at a press conference.
"Important matches are coming up and we have to prepare for the [World Cup] qualifiers."
Messi saved some special words of praise for Alexis Sanchez, who has joined Barcelona from Udinese, saying: "As a person, I do not know him yet, but as a player he has shown all he is in Italy and in the Chile national team.
"He will bring us a lot, he knows the system and he will settle quickly. He is a great signing for us."
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