His team-mates went on to win the match 2-1 but the Barcelona star refused to collect his medal.
Messi was shown a red-card in the 37th minute of the match following a clash with Gary Medel, who was also sent off.
Replays showed Messi nudged Medel as the ball was going out of play but the Chile player reacted by head-butting and barging his opponent.
The 31-year-old merely stood his ground but the referee decided to send both players off.
After the game, Messi said: “There is no doubt, the whole thing is set up for Brazil.
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“I hope the VAR and referees don’t play any part in the final and that Peru can compete but it looks tough to me.
“I did not want to be part of this corruption, we shouldn’t have to be part of this disrespect we suffered during the Copa America.
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“We could have gone further but we weren’t allowed into the final. Corruption, referees and all the rest stopped people from enjoying the football.
“I always tell the truth and I’m honest, that is what keeps me calm, if what I say has repercussions that is not my business.