"The FA of Serbia absolutely refuses and denies that there were any occurrences of racism before and during the match at the stadium in Krusevac," the FSS said on its website.
"Making connection between the seen incident - a fight between members of the two teams - and racism has absolutely no grounding and we consider it to be a total malevolence."
England defender Danny Rose said he was racially abused by Serbia fans before and during the match which England won 1-0 and 2-0 on aggregate to reach next year's European Under-21 Championship finals in Israel.
"Danny Rose behaved in inappropriate, unsportsmanlike and vulgar manner towards the supporters," the statement said.
"By this we inform the overall public that we will, as a matter of urgency, start an internal disciplinary procedure and punish the culprits after reviewing all the reports," it said.
"It will be done whether a possibly disciplinary procedure by the responsible UEFA bodies will be started or not.
"Furthermore, we will not either accept the fact that our players and members of the technical staff were provoked by the gesture of the English player Rose, since violence has no place at sports events. To be honest, we expect the same investigation from the English FA."
