Brazil joined the list of big teams struggling to win their opening matches at the World Cup in Russia.
The five-time champions were held to a 1-1 draw by Switzerland on Sunday.
Philippe Coutinho, who was making his World Cup debut, gave Brazil the lead in the 20th minute with a volley that bounced in off the right post. Steven Zuber then headed in the equalizer in the 50th minute. Mexican referee Cesar Ramos dismissed complaints that Zuber had shoved defender Miranda before getting to the corner from Xherdan Shaqiri.
"There is video of what happened and the referee could have seen it. But it didn't happen," Miranda said.
Ramos also ignored a penalty claim late in the match when Gabriel Jesus was wrestled to the ground by Swiss defender Manuel Akanji.
Switzerland dominated the midfield for long spells against a Brazil team playing its first World Cup match since its 7-1 semifinal loss at home to Germany in 2014.
Serbia 1, Costa Rica 0: Serbian captain Aleksandar Kolarov scored from a left-footed free kick in the 56th minute.
After David Guzman was handed a yellow card, Kolarov curled the ensuing free kick over the wall, and Costa Rica goalkeeper Keylor Navas couldn't reach it.