The 25-year-old has twice featured in friendlies for Brazil - the country of his birth - but he has chosen to play his international football for Spain.
"I do not want to create problems with anyone in Brazil," Costa told Marca. "I want people to accept my decision.
"Would I have a problem scoring for Spain against Brazil in the World Cup final? No."
Costa, who is widely expected to travel with Spain for the 2014 World Cup should they qualify, is close to gaining Spanish nationality.