The forward dismissed reports suggesting the squad lacks quality, while he is hoping that his World Cup performances have not dented his future chances in the national team.
Diego Costa is hoping to continue playing for Spain, despite a poor World Cup campaign.
Costa, who earned a move to Chelsea after scoring 27 goals in 35 appearances in the Primera Division for Atletico Madrid, cannot put his finger on what was missing from the Spain side but rejected claims there was a lack of quality.
The 25-year-old Brazil-born striker opted to play for Spain instead of his birth country and was hoping to fire the team to its fourth successive major championship. However, the team has already bowed out at the group stage of the tournament with one game left to play.
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The Spaniards opened their World Cup campaign with a crushing 5-1 defeat to the Netherlands, before they were defeated 2-0 by Chile on Wednesday to confirm their exit.
"Of course I want to continue with Spain. I dream of achieving the same successes that Spain has already achieved," Costa told Marca. "We apologize, but life goes on. Let us keep working and raise your heads again.
"We had many ambitions. No one is tired of winning. We missed something but it was not quality. It is just true that Chile were physically better than us."
Spain will play Australia, which has also been knocked out of the competition, on Monday 23 June at the Arena da Baixada, Curitiba.