The reigning world and European champions collapsed after taking the lead in their World Cup 2014 opener, as Arjen Robben and Robin van Persie struck twice to fire the Oranje to victory.
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"We're more united than ever. To say that the cycle has come to an end is crazy," said the 28-year-old.
"In football you're forced to move on. We are still full of pride, passion and enthusiasm. We would play Chile today if we could.
"The key to this team has been knowing how to get back up. We cannot go grazy on the back of one result. We're still a great team."
The Real Madrid man also threw his support behind Iker Casillas, who endured a torrid evening between the posts, and backed him to come through his alarming crisis of confidence.
"Bad things can happen even to the best players. I feel bad for Iker but he is motivated and I am convinced he can come back. He will move on from this."
Spain face Chile on Wednesday in what is now a must-win game after the South American side dispatched Australia 3-1 on Friday night.