With Barcelona, Messi has won eight La Liga titles and four Champions Leagues.
But his only major international honour is 2008 Olympic gold, with Argentina now having lost three major finals in three years.
Argentina were beaten 1-0 in the 2014 World Cup final by Germany before two Copa America final defeats by Chile on penalties. Messi was also on the losing side against Brazil in the 2007 Copa America final.
"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," he said.
After Sunday`s match finished 0-0 in 120 minutes, Chile won 4-2 on penalties.
Messi`s miss was Argentina`s first attempt in the shootout and it ballooned over the bar after Sergio Romero had denied Chile`s Arturo Vidal.
Lucas Biglia also missed from 12 yards, with Chilean substitute Francisco Silva scoring the decisive spot-kick in the final in East Rutherford, New Jersey.
Messi had scored five times at the tournament, including a superb free-kick in the semi-final to become his country`s record scorer with 55 goals.
For Barca he has scored 453 times in 531 games, including a La Liga record 312 goals.
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