They also said Danny Rose behaved in an "inappropriate, unsportsmanlike and vulgar manner" towards their fans.
Rose had earlier called for Serbia to be banned after complaining of racial abuse and being hit by missiles during his side's 1-0 win on Tuesday.
The England defender said he had been subjected to monkey taunts long before the violent and chaotic scenes which marred the end of the Euro 2013 play-off.
In a statement on its website, the Serbian FA said: "(The) FA of Serbia absolutely refuses (sic) and denies that there were any occurrences of racism before and during the match at the stadium in Krusevac.
"Making connection between the seen incident - a fight between members of the two teams - and racism has absolutely no ground and we consider it to be a total malevolence.
"Unfortunately, after the fourth minute of the additional time and the victory goal scored by the guest team, unpleasant scenes were seen on the pitch.
"And while most of the English team players celebrated the score, their player number three, Danny Rose, behaved in inappropriate, unsportsmanlike and vulgar manner towards the supporters on the stands at the stadium in Krusevac, and for that he was shown a red card."
The Football Association reported "a number of incidents of racism" to European governing body UEFA after the match.
Rose was sent off after the final whistle for kicking a ball in anger in response to provocation as scuffles broke out involving Serbian supporters, players and other officials.
Rose told Sky Sports News: "I remember getting slapped twice and then I got ushered away.
"That's when I kicked the ball - and the referee sent me off. I don't understand, the game had finished by then but he still sent me off for kicking the ball.
"As I went off again there was monkey chanting, but the monkey chanting started long before I got sent off.
"After 60 minutes my head wasn't really on the game. They have to be banned. I don't understand how else they can learn from it, they have to be banned.''
The Serbian FA maintains they made the England fans and team feel welcome throughout the duration of their stay in the country but following the brawl in the final stages they will now launch an internal investigation.
The statement said: "The Football Association of Serbia apologises to the guests from England and the overall football community because of the unsportsmanlike behaviour of a part of the technical staff and players of the Serbian U-21 team.
"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 will be done whether a 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."
The Serbian FA has supported their belief there were no racist chants during the game as nothing was included in the match reports.
"In support of our statement, there are preliminary reports of the match officials at the match (between) Serbia (and) England.
"None of them mentioned a racist situation and we expect that the human and sports culture of our football friends from England will win over the spread of misinformation."