Liverpool's No.6 played the full game in what was a gripping quarter-final tie.
The quarterfinal at Sochi on Saturday (NZT Sunday) was tied 1-1 after regulation and 2-2 after extra time, forcing both Croatia and Russian Federation to a shootout for the second consecutive game.
The Real Madrid defender said winning the 2018 World Cup would not be easy, in a tournament where "there are no favourites" since "all the remaining teams are strong".
Even before a single ball was kicked in anger, the warning signs were there that this might turn out to be a weird World Cup.
"They are our heroes, they are our inspiration, they brought us to this point, and we would like to continue on their way, and hopefully we will take a step further tomorrow if we have the strength and luck to do so", he added. We have to enjoy the moment, then tomorrow we prepare for England, we have one day less for preparation.
Croatia coach Zlatko Dalic said Subasic's uncertain health had affected his substitution management going into extra time.
When he bought a ticket past year for a World Cup quarter-final in Sochi, Russian soccer fan Yevgeny Yegorov guessed, based on form and pedigree, that he would most likely be a neutral spectator watching Spain play Argentina.
The 90 minutes ended 1-1 before the referee signaled for the start of the extra time.
They will have to play much better, " said Reuters ahead of the game. "When you've got all these other teams, France, Belgium, England, that's the top teams from the beginning and we are the underdogs".
A comedian who had denigrated Russia's World Cup soccer team in a music video apologized last month after they reached the knockout stage. We made ourselves happy but we also made everybody back home in Croatia happy.
But with five minutes to go before the end of extra time Mario Fernandes scored to force penalties.
In group play, Croatia were more impressive than England, as it won all three of its matches, including a 3-0 drubbing of Argentina.
"He could go on and that was the most important thing", Croatia captain Luka Modric said at fulltime. The favourites, the big teams are home.
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