The Spain shot-stopper admitted he was well below par during their Group B opener as Louis van Gaal's side romped to a 5-1 victory over the world champions on Friday
Louis van Gaal's side recovered from falling behind to a first-half Xabi Alonso penalty, with Arjen Robben and Robin van Persie both scoring twice and Stefan De Vrij adding another to avenge the 1-0 defeat the Dutch suffered in the final of the 2010 World Cup.
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"It's time to be quiet, to reflect and think about the next match against Chile as a final," the 33-year-old was quoted as saying by Marca.
"We apologise, and I am the first in line. Our fans must give out the criticism that comes to us and forget what happened soon.
"I have not been up to par and I accept that. We have not been fortunate, starting with me. Now only we think about the next game.
"I have to take the blame. All we could do is think about the next game when they scored the third goal and went further behind. I am mature enough to receive all criticism. We must sort ourselves out."
La Roja boss Vicente Del Bosque, however, insisted that no one player should shoulder the burden of responsibility for the loss, especially not their goalkeeper.
"When a team loses a match it's not just the performance of one single player, it's a weakness in the total squad," the 63-year-old said.
"We can't blame anyone, least of all Iker Casillas."
Spain, who sit bottom of Group B after the first round of games, face Chile on June 18, who beat Australia 3-1 in their first match.