It was the first time Messi made three assists in a single game for his country and only the second time in his career after he achieved the feat playing for Barcelona in a King's Cup match against Levante in January 2014.
The 28-year-old has 31 assists for club and country so far in 2014-15, two short of his record of 33 from 2011-12.
"It really doesn't bother me that I am not scoring," Messi told reporters after the match in Concepcion.
"Hopefully my goal will come in the final," he added.
"The important thing is to lift the national team as high as possible and it doesn't matter who gets the goals."
Messi is attempting to win the Copa America to cap a superb season when he helped Barca win a treble of Champions League and domestic league and Cup titles.
He has bounced back in style from a disappointing 2013-14 campaign, when Barca failed to collect major silverware and Argentina were beaten 1-0 by Germany in the World Cup final.
Argentina are trying to win the Copa America for the first time since 1993, having lost to Brazil in 2004 and 2007 before being knocked out on penalties in the quarter-finals on home soil in 2011.
"Winning the Copa America would round off something spectacular," Messi said.
"I think we are coming into the match in good shape, but we will be playing a team with very good individual players.
"Both sides always try to play good football and not leave the opponent any time on the ball."
If he wants to score in Saturday's final, Messi knows the man in the Chile goal he will have to beat very well: Barcelona team mate Claudio Bravo.
(Writing by Iain Rogers, editing by Sudipto Ganguly)
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