Perenial shootout losers England were up next, taking on Colombia in the round of 16.
Belgium and Croatia will now be seeking a first World Cup final appearance, while France could reach a third after 1998 and 2006, and England have to go back to Wembley 1966 for their one and only final.
Croatia will next play England in the semifinals on Wednesday in Moscow.
'Of course there is some power left for the English, ' he told a post-match press conference. At that time, we had a lot of players at the best clubs in the world, and that's the case now so we are happy.
England take on Croatia on Wednesday in Moscow in another match in which the shifting sands of tournament play now make it hard to pick a clear favourite. We're giving our all. "They are still great guys for us, they are heroes", said Peskov. "We don't want to stop". They have a young, alive, attacking team.
The Russians as hosts did not need to qualify for the World Cup and their ranking of 70 in the world was the lowest among all teams in Russia, even lower than worldwide football minnows Saudi Arabia.
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On a scorching Saturday that saw England advance further in the World Cup than the home of the handsome game has since 1990 and Croatia take down a dynamo, Russian Federation was on seemingly everyone's lips yesterday - and we don't mean Robert Mueller's ongoing investigation of Donald Trump and the adjoining array of Congressional committees.
The first to speak to the fans was the team's chief coach Stanislav Cherchesov who thanked all those who had supported the team.
At this stage of the tournament, there are only four days between matches. Croatia will go into the game as favourites but Dalic is not underestimating the hosts.
"I wasn't born the last time England reached a World Cup semi-final (in 1990)", England keeper Jordan Pickford pointed out when asked about past glories.
"Russia has shown the world what kind of championship we can have - the best in the world", said another fan.
He added that he would have retired as professional footballer earlier if not for the World Cup and now plans to become a coach.
The Russians were the lowest-ranked of the 32 teams at the World Cup but, just as in the previous round against Spain, they refused to die despite enjoying just 36 percent of possession against a superior Croatian team.
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