Speaking directly after the final whistle, Ramos said his team had given everything they could only to come out on the wrong end of the spot-kick "lottery".
Russia's penalty shootout hero, goalkeeper Igor Akinfeev, thanked God, luck and the Luzhniki Stadium crowd for bringing the hosts home safely against Spain on Sunday to reach their first World Cup quarter-final since 1970.
"It's very hard", Ramos said, as per ESPN.
Kremlin spokesman Dmitry Peskov said, after Russian Federation knocked the 2010 champions out on penalties in Moscow's Luzhniki Stadium, that Putin - who watched the game on TV - had not put any pressure on the team to win.
Spain led in the 12th minute when Ramos helped force Russia's Sergei Ignashevich into an own goal when his back was turned to the play.
Spain captain Ramos, who said it was "very hard" to take his country's "painful" World Cup exit, did not address his own future plans but said he was sure his national side would be back competing for trophies at the next worldwide tournaments.
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Pique has played every minute of Spain's campaign so far and is looking for his second World Cup title triumph after succeeding with the national team back in 2010.
Spanish midfielder Andreas Iniesta thanks the crowd after the game.
On a central Moscow square, a street orchestra erupted in a rendition of the Russian anthem as passing cars tooted their horns and men staggered out of a nearby bar waving Russian flags.
A Russian fan celebrates his team's win over Spain in the World Cup. "We had great hopes for this World Cup and it wasn't to be".
"I haven't regretted that decision or any other, because they are decisions made with responsibility, conviction and values, and it was not a sporting decision", the federation president said.
"Penalties are a lottery - and we lost today, but I am very proud of these players as captain".