Croatia captain Luka Modric said his side showed character on Saturday to get through "another drama" after edging to a second straight shootout win to knock out Russian Federation and set up a World Cup semi-final with England.
The match had ended 2-2 after extra-time after Mario Fernandes' late equalizer for Sbornaya.
The victor will book their place in the World Cup final against either Belgium or France.
Croatian defender Domagoj Vida and ex-national team member Ognjen Vukojevic, both former players of Dynamo Kyiv, recorded a video address to Ukrainian fans after Croatia defeated Russian Federation in a dramatic penalty shoot-out that crowned the historic quarterfinal at a Sochi stadium.
After finishing at 2-2 at the end of regulation time, Croatia and Russian Federation headed into the penalty shoot-out to decide the victor which will face England in the semi-final next Wednesday.
"Of course there's power left for the English", Croatia coach Zlatko Dalic said.
The screamer came in the 31st minute at Fisht Stadium. Croatia began warming up its backup goalkeepers in case Subasic was unable to continue into extra time.
"Modric is bestselling, although (Danijel) Subasic is becoming increasingly popular", Ana Maric, 20, selling souvenirs in downtown Zagreb, told AFP. And defender Sime Vrsaljko has been replaced in extra time after going down away from the action and pointing at his left knee. However, Croatia had other plans and went unbeaten to win the group impressively.
This is an opportunity to go one step further than Croatia reached at the 1998 World Cup, where a team managed by Miroslav Blazevic and including Slaven Bilic and Davor Suker reached the semi-final.
Croatia will play England in the semi-final on Wednesday and some Russian officials had called on football governing body FIFA to take tough disciplinary measures.
Russia's unexpected run to the quarterfinals sparked a surge of support from fans who had largely been indifferent to the team before the World Cup started.
The World Cup hosts were not given any chance prior to the kickoff of the Mundial but they surprised many right from their opening game when they pumped in five goals against Saudi Arabia.
"I am playing at the World Cup".
With the semifinals and the final yet to be played, the knockout stages of the 2018 World Cup have already produced 35 goals, three more than the entire knockout phase four years ago in Brazil.