"They were dying on the pitch, we are proud with them", Kremlin spokesman Dmitry Peskov is quoted as saying by Interfax.
He also netted in the subsequent penalty shootout.
Croatia's shootout victory over Russian Federation was their second straight win on penalties at the World Cup, having beaten Denmark in the same fashion in the last-16, and Dalic admitted that playing 120 minutes twice in the last six days was not ideal, particularly as some of his players are now carrying injuries.
"Glory to Ukraine! This victory is for Dynamo and for Ukraine", he chanted in the video, alongside Dynamo Kiev scout and former Croatia global Ognjen Vukojevic.
Vida was part of one of Ukraine's top clubs, Dynamo Kyiv, from 2013 to 2017.
Vida will be pleased that he has been just as lucky, as his side prepare to take on England in the semi-finals on Wednesday.
Croatia's first female president Kolinda Grabar-Kitarovic's celebratory gestures during her nation's win over Russian Federation in the FIFA World Cup 2018 at the Fisht Stadium in Sochi went viral on social media.
Spartak Moscow winger Alexander Samedov also confirmed he is retiring from global football after Russia's defeat.
Having realised the huge negative reaction his video received, Vida has spoken to Sports.ru in a bid to play down the situation and justify his reasons for the words he used.
The 51-year-old coach, who has only been in charge of the national side since October, said: "I wouldn't say there are any glaring weaknesses - they are in the semi-finals, that says it all".
It did not take too long for Croatia to get back on track as Mandzukic turned provider for the equaliser, charging down the left and pulling back for an Andrej Kramaric free header from seven yards. It wasn't immediately clear whether they intended the video to be made public, or if it was a personal message later uploaded to YouTube by someone else.
Pope consoles Brazil fans * Goal-fest?
The pope, an Argentine and an avid soccer fan, noted a preponderance of Brazilian flags on display in St. Peter's Square during his traditional Sunday blessing. Argentina was eliminated from World Cup contention in the first of the knockout rounds.