Vicente del Bosque's side have now earned the distinction of becoming the first international team in history to surrender their world title after just two group stage fixtures.
"When things don't go your way, it's never because you don't want to win because we all want to win here," the Barcelona playmaker told reporters.
"Everyone should be a leader but we weren't on top of the situation.
"It feels very cruel for the moment. It's a very difficult moment. If this team wins something it's for sporting reasons but we didn't do it. It hurts a lot because the excitement was tremendous."
Spain conclude their tournament by facing Australia - who have also been eliminated - on Monday, while Netherlands and Chile battle it out for top spot in Group B.