Niko Kovac's men drew 1-1 against Italy in a Euro 2016 qualifier on Sunday, but the clash was overshadowed by flare-throwing visiting fans at San Siro in Milan.
The encounter, which Croatia were praised for dominating, was postponed twice and almost abandoned.
In a statement titled 'Let's put an end to hooliganism' and published on the federation's website on Monday, the HNS called for action to be taken.
Like coach Kovac, the HNS apologised and said it had taken all possible action in the lead-up to the game to stop hooliganism.
"HNS calls for Croatian authorities to prosecute all hooligans who took part in the incident because their law on the prevention of violence at sporting events make it possible," a statement read.
"We invite all other segments of Croatian society, beginning with the Croatian government and all the institutes of the Republic of Croatia, that these incidents that shame the country and Croatian football are seen as the 'last drop in the glass' and that will inspire all those who have the power to contribute to the solution of problems."
