Vida, who scored in the match against Russia - which ended 2-2 after extra time - and netted in the resulting penalty shootout, later said of his comment in quotes reported by Russian outlet Championat: "I respect the Russian nation".
Croatia'sDomagoj Vida can play against England in Wednesday's World Cup semi-final despite featuring in a pro-Ukraine video.
The Croatian football federation has removed Ognjen Vukojevic from the team's World Cup coaching staff after he was filmed dedicating the quarter-final win against Russia to Ukraine.
Earlier, NAIJ.com had reported how Croatia president Kolinda Grabar-Kitarovic rushed into the dressing room to celebrate with the players after their penalty win over Russian Federation.
"I would never want to be a burden to the national team, especially not ahead of a match as monumental as the World Cup semi-final, when the team is most in need of a peaceful atmosphere", Vukojevic said.
It wasn't immediately clear whether Vida and Vukojevic intended the video to be made public, or if it was later uploaded to YouTube by someone else.
In their full statement, HNS said: "Vukojević published a controversial video on social media after the match between Croatia and Russian Federation in the quarter-final of the FIFA World Cup".
"There's no politics in football".
During the ongoing 2018 FIFA World Cup in Russian Federation, the hosting national football team managed to make it to the quarterfinals stage, where Croatia edged them out on a 4-2 penalty shootout to close Saturday's spectacular match in Sochi.
And the Besiktas centre-back has explained his comments were meant purely as a message of gratitude for the support he has received from fans of his former club Dynamo Kiev.
The Croatian FA had issued a press statement on Sunday attempting to clarify the incident and calling on players to avoid sending messages that could be deemed to be politically provocative.
Vukojević started to play football at Mladost Ždralovi and moved to NK Bjelovar before starting his professional career at Slaven Belupo in 2003.
"However, I do understand that my statements can be differently interpreted, " he said. Precisely, Ognjen Vukojević, who was one of the Dalić's associates, was asked to leave the Croatian delegation on Monday, reports Gol.hr on July 9, 2018. Earlier, FIFA fined but did not suspend two Swiss players for celebrating goals by making a gesture in the sign of a double-headed eagle - a symbol of Albania.