The Real Madrid winger was suspended due to an accumulation of yellow cards and watched from the stands as Brazil lost to record 15-time winners Uruguay 4-2 in a penalty shootout following a goalless draw on Saturday.
Brazil had failed to impress at the Copa, drawing twice in the group stage while beating only Paraguay.
It was their second straight quarter-final exit from a major tournament after they lost to Croatia on penalties at the 2022 World Cup in Qatar.
"The Copa América is over and it's time to reflect, to know how to deal with defeat," Vinicius posted on Instagram. "The feeling of frustration takes over again. Again on penalties.
"I failed to pick up two avoidable yellow cards. Once again, I watched the elimination from the sidelines. But this time, it was my fault. I apologise for that. I know how to listen to criticism and, believe me, the harshest criticism comes from home.
"Fortunately, my career with the national team has only just begun. Together with my teammates, I'll have the chance to put our national team back where it belongs. We'll get back to the top! I love you and let's go together!"
Vinicius, who enjoyed a fine 2023-24 season at Madrid, has scored five goals in 34 appearances for Brazil since making his international debut in 2019.
