The 25-year-old won a first-half penalty for La Roja in the Group B clash, but the European and world champions then conceded five times without reply against Louis van Gaal's side.
Costa, however, is still confident that Spain will advance from their group.
"We still have options. The good thing about life is that there is always a chance. We have to take it and fight to the end," the forward told SportYou.
"Chile is the game of our lives to stay alive in the World Cup. Nobody likes to lose and much less in the way we did. But people know that we can't give up because we still have possibilities.
"We must learn from the defeat and it can serve as a lesson to not happen again."
Costa is widely expected to join Chelsea after the World Cup.