Other players took turns thanking supporters before the ceremony ended with a rousing rendition of the Russian national anthem.
Denis Cheryshev, who scored his fourth goal of the tournament when he gave Russian Federation the lead with a rasping left-footer from the edge of the box in the 31st minute, said the players left their all on the field.
Now they are looking to go one step further, but just getting this far is a source of great pride for Croatia. "We will enjoy this game and hopefully we can make history".
Croatia captain Luka Modric said his side showed character on Saturday to get through "another drama" after edging to a second straight shoot-out win to knock Russian Federation out of the World Cup and set up a semi-final with England.
They had also needed spot kicks to get past a dogged Denmark in the last 16, but Modric insisted they would not be exhausted for the last-four clash against England.
The teams then traded two scores each before Ivan Rakitic converted the winning penalty.
"For us, the most important thing is we've reached the quarter-finals". At some point, that wave could crash. You have to pay the toll for such exertions.
Meanwhile, Dele Alli, who scored England's second goal, said it was a great team performance.
Bringing the 24-year-old winger back into the worldwide fold has been one of the changes made by Dalic, who replaced Ante Cacic as coach late last year.
The 29-year-old Besiktas center-back headed Croatia in front in extra time after Denis Cheryshev netted his fourth goal of the tournament to put Russian Federation 1-0 ahead Andrej Kramaric equalised, only for Mario Fernandes to dramatically send the game to penalties. We played at club level as well, ' says striker Mario Mandzukic, who played with Modric at Dinamo Zagreb a decade ago before the latter joined Tottenham Hotspur. "We made ourselves happy but we also made everybody back home in Croatia happy". I don't cry often but now I have a good cause: Croatia are in the semi-finals. All photos were taken on Board the aircraft that the team flew from Sochi to Moscow.
Sixteen of Dalic's squad play in Europe's big five leagues, with Monaco goalkeeper Danijel Subasic the hero against Denmark when he saved three penalties. The unique elements of playing in Sochi with the combination of heat and humidity sapped energy from both teams, creating a fairly lethargic second half.
"Moscow, Croatians are arriving!"