The Barcelona midfielder was shown a straight red card towards the end of the first half following a confrontation with former Cardiff midfielder Gary Medel, who was also dismissed.
"I didn't go to the podium because we shouldn't be part of the corruption and lack of respect", he said.
Incredibly, Paraguayan referee Mario Diaz de Vivar showed the two captains the red card.
Messi raged afterwards at the decision to send him and Medel off, saying: "I think the referee overreacted".
Paulo Dybala praised Lionel Messi for the lucky charm that he handed to him ahead of scoring his first competitive goal for Argentina.
Despite the defeat of Peru, the Chileans, as a team, in general, at this tournament look much stronger than the Argentines, so it makes sense to count in this meeting to win them.
The match with "pentakampeonami" could not be held at the highest level - the hosts of the tournament won 2-0 and went to the final.
Argentina lost 2-0 to Brazil in the semi-final of the competition, with La Albiceleste lodging an official complaint for the officiating in that tie. "I hope that the VAR and the referees have nothing to do and that Peru can compete because they have the team to win, but I see it hard". I think the referee overreacted.
Arturo Vidal halved the deficit from the penalty spot in the second half but that wasn't enough for Chile to pip Argentina. It was only the second red card of Messi's career. "It seems to me that they are not yet clear about the VAR system", he said at a press conference.
South American football bosses say accusations questioning the integrity of the Copa America are "unfounded" and "represent a lack of respect".
The governing body said that "a fundamental pillar of fair play is accepting results with loyalty and respect".
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