"It's a reality that this is my last game with the national team, on a wonderful stage", said Iniesta, a member of the 2010 World Cup winning Spanish squad.
Igor Akinfeev was the name on fans' lips in the capital after the Russian goalkeeper and captain saved two penalties in the 4-3 shootout, including Spain's final effort which he stopped with a trailing foot.
He also said the Federation would now look at what direction to take with regards the next Spain coach.
With players such as world-class midfielder Luca Modric and a string of top-level forwards including Mario Mandzukic, Ante Rebic, Andrej Kramaric and Ivan Perisic, Croatia will challenge Russia's backline far more than Spain's lackluster Diego Costa did in the entire game.
"[Cristiano] is one of the two best players in the world", he said. "I am very grateful for one of the greatest players in our history".
Rubiales has another hard decision to make now - whether to keep Hierro or bring on another coach to continue revamping the national team.
Dzyuba, unable to contain his delight after keeping his nerve to plant the equalizer past David de Gea after Gerard Pique's handball, said he found stepping up to take the penalty intimidating but that the heavens had been on his side.
It remains unclear if Hierro will, or indeed wants to, stay on or if the RFEF opt to go in a different direction.
Just as it remained unclear whether he would actually remain in charge, so it's still all up in the air for Spain a day after its latest World Cup debacle. Goalkeeper Danijel Subasic was the hero, saving three spot-kicks after the match finished 1-1 following extra time.
Russian Federation had already defied expectations by reaching the World Cup last 16 for the first time since the collapse of the Soviet Union but after victory over Spain fans now believe the tournament's lowest-ranked team could go all the way.
Mighty Spain dominated the field at Luzhniki Stadium, dulled the senses with mind-numbing ball movement around the perimeter of the penalty area Sunday.