Despite leading La Roja out of their group in Russia, Hierro was unable to prevent his side from losing on penalties to the hosts in the last 16.
"We all feel pain, we came to do something important, fight for the World Cup, but that's football," Hierro told Football Espana after the game.
"It's nothing to do with their commitment, companionship and effort they put in every day.
"It's been a pleasure to coach them. If there's anything to criticise us for, I'm the coach and I'm the one most responsible for what's happened.
"My future? It's not my decision whether I stay. After this elimination, what I do doesn't matter."
Spain won the World Cup in 2010 but were knocked out at the first hurdle four years later.