The 23-year-old received a straight red card when he attempted to headbutt Colombian stopper Jeison Murillo after the full-time whistle before then landing himself in further trouble by insulting referee Enrique Osses in the tunnel.
Neymar was subsequently hit with a four-game suspension, thus depriving Brazil of their captain for the remainder of their Copa America campaign.
While Selecao team-mate Alves insists that the ban was excessive, the defender conceded that his young compatriot has to start handling provocation better.
"I told him to be quiet and learn from all this so he doesn’t repeat these mistakes, which have ultimately hurt Brazil," Dani Alves told reporters after the match.
"The punishment was too severe. If it had been another player then there would not have been such an impact. It’s bad for us as we’ve lost our difference-maker.
"He’s a player who gets kicked around, but we don’t give [those things] importance. Football is far more beautiful than that, it’s about the great moves and goals."
The Brazilian Football Confederation confirmed on Monday that Neymar would leave the country following their decision not to appeal for a reduction to the ban.