Hierro was parachuted in as coach a day before the tournament got underway after Royal Spanish Football Federation (RFEF) chief Luis Rubiales opted to sack Julen Lopetegui for failing to keep him abreast of a move to Real Madrid.
The 50-year-old Hierro guided Spain through the group phase but his team could not conjure up a winner despite 120 minutes of domination against a Russia side who prevailed 4-3 in a penalty shoot-out in their last-16 tie following Sunday's 1-1 draw.
Former Spain defender Hierro was not interested in discussing his own future in the immediate aftermath but said he took full responsibility for what happened in Moscow.
Asked if he blamed the Federation, he said: "No, we can't go finger pointing and laying blame. We need to be realistic, the situation was what it was.
"It's completely pointless to analyse the past, we made the decisions we made but I am not going to lay blame at the feet of other people.
"I took on this role out of a sense of responsibility and I accepted it with all its consequences.
"I will be honest, I am leaving resting easy. I think we all tried to give our best, the players, the staff, everyone that helped to contribute. This is football."
Hoy hemos caído.— Selección Española de Fútbol (@SeFutbol) July 1, 2018
Pero nos levantaremos, como siempre hemos hecho.
Ahora más que nunca... ¡¡VAMOS, ESPAÑA!!🇪🇸 pic.twitter.com/jeTTVStJ5y
It remains unclear if Hierro will, or indeed wants to, stay on or if the RFEF opt to go in a different direction.
He added: "Honestly, that does not worry me, I don’t think it's important right now.
"Now we need to share this difficult moment. We wanted to do great things, this is a generation of extraordinary players.
"This is the fruit of two years of work, of Lopetegui's work, and yet we are out despite not losing for 24 games. If anyone should shoulder this responsibility it is me. I put my reputation out there because that’s what my job required."
Hierro was certainly not looking to blame any of his players, who he said had given their all.
"In my last message before the game I told them this is a World Cup, enjoy the experience, and let's leave the match with our heads held high," he said. "They certainly did that, and we can look each other in the eye.
"The whole 23 of them have been great, they have worked hard, they have great solidarity, they are great professionals. I am not holding anything against my players, the 15 that played gave it their all. Unfortunately, it ended up as a penalty shoot-out which is a lottery and we weren’t lucky."
Hierro showed he was not afraid to make a major call after leaving Andres Iniesta, the hero of their 2010 World Cup triumph, on the bench.
He was introduced midway through the second half and Hierro was hugely impressed by the way he dealt with the disappointment on what turned out to be his final Spain appearance.
"I left him out because I knew what this match required," he said. "I am very grateful for one of the greatest players in our history. I told him what I had to and that will stay between the two of us.
"If we look at how he played, he was an example, he was a professional, he played the first three games and we knew this could be a long game.
"I would give him a 10 out of 10 [for his performance]. He is an outstanding professional and I'd like to thank him again for the way he behaved. He played as though it was his first cap."