The Barcelona forward clashed with Gary Medel in the first half of the match, with both players given their marching orders after coming together and the former appearing to aim a headbutt at his opponent.
Messi sounded off against the South American federation earlier this month, but they have responded with a negligible fine and no further suspension beyond the automatic one-game punishment for a red card.
After being sent off against Chile, Messi skipped the Copa America medal ceremony, clearly still upset about his red card in the third-place game and what transpired in his nation’s semi-final defeat to host country Brazil.
"There is no doubt, the whole thing is set up for Brazil," Messi claimed in relation to the controversial VAR decisions that went against Argentina in the semi-final loss to Brazil.
"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.
"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."
Brazil would go on to defeat Peru 3-1 in the final to lift the Copa America on home soil.
CONMEBOL responded to Messi’s comments with a withering statement of their own, accusing the Barcelona star of a "lack of respect".
"In football sometimes you win and sometimes you lose and accepting the outcome of a match with loyalty and respect is a fundamental pillar of fair play. Same goes to the refereeing decisions, that are human and will never be perfect," the statement read.
"Said accusations represent a lack of respect for the competition, all the football players involved and the hundreds of professionals of CONMEBOL, an institution that since 2016 has been tirelessly working to professionalise and develop South American football."
If Messi was bothered at all by the fine he received on Tuesday he wasn’t showing it.
Immediately after the punishment was announced he posted a picture on Instagram showing how he was enjoying his summer time off with his family and friends.