Messi hit out at CONMEBOL and the tournament as a whole following the semi-final defeat and once again after Argentina's third-place clash with Chile, a match that saw the Barcelona star sent off under dubious circumstances.
Messi suggested the officials had been favouring the tournament hosts throughout the competition.
The Argentinian forward was particularly critical of the efforts from the Video Assistant Referee and match official Roddy Zambrano, as he used a post-match interview to criticise the decision to not award a penalty to Sergio Aguero.
He once again was critical following a red card in the third-place match, as Messi was sent off for a confrontation with Chile midfielder Gary Medel in which Messi was far from the aggressor.
The claims were slammed by CONMEBOL, who called Messi's rant "unacceptable" after the forward railed against "corruption" and "a lack of respect" following his red card against the two-time reigning champions.
Messi's comments also prompted Brazil boss Tite to step in and say that a star of the 32-year-old's magnitude needs to show more respect.
And Alves echoed his coach's sentiments, reiterating that Messi remains a dear friend, but a friend that he believes was in the wrong.
"A friend is not always right just because he's a friend. You can say it in the heat of the moment, but I still won't agree," Alves told SporTV's 'Bem Amigos' .
"Firstly, he's disrespecting an institution such as the Selecao, in my view. Secondly, he's being disrespectful with several professionals who put a lot of things aside so they could be there fighting for a dream.
"I'm a friend who always tells the truth when it's due, and I think he was wrong for saying these things."
Alves also went on to defend Brazil team-mate Neymar, who missed out on the Copa America due to an injury suffered in a pre-tournament friendly against Qatar.
The 36-year-old, whose contract at Paris Saint-Germain has expired, backed his team-mate as one of the game's best in the wake of criticism after Neymar skipped out on the Ligue 1 champions' first training session of pre-season.