The Venezuela boss has accused Japan of a "lack of respect" for sending an under-23 side to the tournament and called for an end to the policy of invites.
Venezuela head coach Rafael Dudamel accused Japan of showing a lack of respect and has called on Copa América organisers to stop asking non-South American teams to participate.
CONMEBOL has a history of inviting nations from outside the continent to compete in the tournament, with Japan and Asian champions Qatar being selected this time around to make it a 12-team format.
Japan, who also took part in the 1999 edition, are using the competition as preparation for the Tokyo Olympics next year and have sent a team made up of under-23 players.
And Dudamel has joined Paraguay boss Eduardo Berizzo in questioning the Samurai Blue's participation in Brazil.
"I think the Copa America has to be of CONMEBOL, of the South American teams," Dudamel said at his news conference following Saturday's 3-1 win over Bolivia.
"I do not agree with the invitation to Japan, which used their under-23 players. I consider it a lack of respect for our competition.
"Like other colleagues, I state my position. The Copa America has to be from CONMEBOL and the South American teams."
Villegas: "It's good that Copa América has invited guests"
GRUPO A: O Brasil goleou e terminou como líder do Grupo A, a Venezuela venceu a Bolívia e é a segunda, o Peru em terceiro lugar terá que esperar pelo final da fase de grupos. A Bolívia em último lugar se despede da @CONMEBOL #CopaAmerica. pic.twitter.com/aWvaJSX573— Copa América (@CopaAmerica) June 22, 2019
Japan and Qatar are still in with a chance of reaching the knockout stages heading into their final round-robin fixtures, against Ecuador and Argentina respectively.
Bolivia became the first side to crash out of the tournament with their defeat to Venezuela, but head coach Eduardo Villegas is happy for teams from around the world to take part.
"I consider it a good thing that Copa América has invited guests," Villegas said. "I think it's favourable that the Latin American competition has Asian teams.
"When we played with [South] Korea and Japan in friendlies, we were surprised by the dynamics of their football. And so I consider these countries playing in South America very positive."