The Selecao chief says Luiz Felipe Scolari's men will survive without the Atletico Madrid forward.
Brazil does not need Diego Costa and respects his decision to play for Spain, according to technical director Carlos Alberto Parreira.
The 25-year-old, who has represented the Selecao on two occasions, was granted Spanish citizenship in 2013 after moving to the country in 2007 and has since made it clear that he would like to play for the current world champions.
Brazil plays South Africa in a friendly Wednesday and, though Parreira has said that Costa would be a valuable squad member, the national team's chief believes his side will not be too disadvantaged without the in-form Atletico Madrid striker.
"Diego Costa has been with us once, even twice he actually played. And then for a certain period we didn’t select him because we had to look at so many other players, but he was in our sight," the 71-year-old told reporters. "Then, when we decided to bring him back for the Confederations Cup, he had already made the decision as he was invited for the Spain national team.
"He made his decision and we have to respect it. He is not a Brazilian player any more. He made his decision to play for Spain, but Brazil will survive without him, don’t worry. He is a good player, we would like to have him but we are not going to be crying and say how we miss him. There is life after him."
The 71-year-old also insisted that there is belief that coach Luiz Felipe Scolari can guide Brazil to a sixth World Cup and thinks that home advantage will be crucial in the nation's attempt to topple Spain.
"We are playing at home with confidence and with the players we have we are really thinking about winning it," he added. "We have experience and the people behind us as they were in the Confederations Cup — that was a really wonderful mood which I have never seen in Brazil before.
"We can focus on the World Cup with the energy of the people behind us, and you cannot believe how important that is. After 1950, when we did not win the World Cup at home, we have a second opportunity and we do not want to miss it."