Messi blasted his penalty over the bar as Chile won the tournament for the second successive year following a goalless 120 minutes.
Messi cut a dejected figure after Argentina’s trophy drought at senior level was extended to 23 years.
It was the fourth final he had lost with his country.
He said: “In the dressing room I thought that this is the end for me with the national team, it’s not for me.
“I tried so hard to be champion with Argentina. Now I am leaving without having managed it.”