The Argentinian security ministry said in a statement it had identified four Argentinian fans in the video and it would "ask Russian authorities to immediately detain them so they can be deported".
Daria also said that her team of bakers was constantly in touch with the footballer's representative about handling his sculpture, which they placed on top of the mouth-watering cake.
"What's happening to the team right now is what has happened to Argentina in these last four disgraceful years: anarchy, no leadership from the players, coaches or directors".
Simeone meanwhile was scathing of error-prone goalkeeper Willy Caballero, whose howler led to Croatia's opening goal.
It was an ugly performance all around for Argentina, as they struggled to get their stars, Messi and Sergio Aguero into the proceedings . "If you have to choose between Messi and Ronaldo in a normal game, who would you choose?" said Simeone.More news: Japanese fans tidy up stadium after win over Colombia
Argentina's struggles in Russian Federation should come as no surprise after their pre-tournament preparations were wrecked by controversy and poor form, coupled with a reliance on a top-heavy, limited squad. Argentina faces an early World Cup exit after picking just one point from two league matches. On Thursday they staged an epic second half collapse on their way to losing 3-0 to Croatia. I think it's unusual because he is a very important player in the national team and he had little involvement, which is odd.
Soccer's world governing body Federation Internationale de Football Association said earlier on Friday it was trying to identify the fans, who were filmed fighting at Thursday's World Cup match between Argentina and Croatia in Nizhny Novgorod.
Mario Kempes, a 1978 World Cup victor with Argentina and analyst for ESPN, tweeted: "The spectacle was shameful and the farewell is increasingly closer!"
He added that Sampaoli now has a crucial task now to rebuild his team's confidence ahead of Tuesday's crucial game against Nigeria.
"Messi, who keeps winning for Barcelona, who continues to deliver triumph after triumph for Barcelona, has given us nothing but defeats and sadness", said Miguel Angel Gutierrez, a 50-year-old Argentina supporter in Buenos Aires.
On a closer look, scores of fans across the globe are hoping for a good show from Messi in the coming days.