Russia progressed to the quarter-finals on home soil after a 4-3 penalty shoot-out win that followed a 1-1 draw in Moscow.
Spain dominated the game without creating clear chances, with Artem Dzyuba’s penalty cancelling out an own goal from veteran defender Sergei Ignashevich in the first half.
Ramos was one of three Spain players to convert their penalties in the shoot-out as Koke and Iago Aspas saw efforts saved by Russia hero Igor Akinfeev.
Andres Iniesta has already confirmed he is retiring from international football in the wake of the defeat, while Gerard Pique previously announced Russia 2018 would be his last international tournament.
And Ramos hinted at a further turnover of players, although the Real Madrid centre-back intends to play on towards Qatar 2022.
“It hurts a lot, but no one doubts that we will try again and again and again,” Ramos posted on Twitter.
“Some will leave and others will come but we will all defend this shirt with passion and respect.
“In defeats is when I feel most proud of being Spanish.”
Ramos’ fellow Madrid defender Nacho Fernandez also pledged to help 2010 champions Spain return to the summit of the sport.
“Our dream was to get another star for our country,” Nacho wrote on Twitter. “Football never prepares you for such moments.
“But this team will rise as Spain always does. Proud to be part of this group and much more now.
“Life goes on … And there we will be ALL to fight.”