The Serbian hosts were charged by UEFA with misconduct over the racial abuse its fans allegedly hurled at England players from before kickoff in Krusevac on Tuesday night.
But both federations face action for "improper conduct" over the scuffles that broke out on the pitch between the teams after the match, which England won 1-0 to secure qualification for the 2013 European Under-21 Championship.
The cases will be heard by UEFA's control and disciplinary board on Nov. 22.
In Belgrade, Serbia's prime minister Ivica Dacic ordered a police probe, saying all those who took part in the scuffles must be identified and brought to justice.
The bitterness between the two nations was emphasized by their respective statements Wednesday, with the English Football Association suggesting it might decline to send teams to the Balkan nation in the future and the Serbians emphatically denying racism and denouncing the visiting players.
But the FA was backed by the British government strongly condemning Serbia and writing to UEFA President Michel Platini on Wednesday demanding "tough sanctions."
"A number of England players were subject to extreme provocation and racism," sports minister Hugh Robertson wrote to Platini.
British Prime Minister David Cameron was also said by his Downing Street office to be "appalled by the scenes."
"We are determined to stamp out racism overseas and at home and we are giving full backing to the FA's complaint," said Cameron's spokesman, Steve Field. "If we are going to stamp out racism from football then it is no good handing out derisory fines as has happened in the past."
In 2007, UEFA fined Serbia €24,000 (then $32,600) after its players and fans hurled racist abuse during another under-21 game against England.
In a reference to a much-criticized suggestion by FIFA President Sepp Blatter last year, Field said: "It is no good telling players to shake hands and forget about it."
Blatter said later on Twitter that he is "saddened every time I hear about racist incidents in football."
But the Serbian FA denied in a statement that there was any racial abuse "before or during the match" of England players, who had extra security personnel brought by the FA due to fears about their safety.
Serbia laid the blame for the incidents after the final whistle squarely on England defender Danny Rose, claiming he "behaved in inappropriate, unsportsmanlike and vulgar manner towards the supporters for which he was shown a red card."
"Unfortunately, that led to the incident that followed," the Serbian FA statement said.
The English FA responded with a statement insisting its players and staff "were subjected to racial abuse, violence as well as missiles" throughout the match.
"FA officials made UEFA officials aware of racist abuse from sections of the crowd aimed at a number of England's black players at halftime on Tuesday evening," FA General Secretary Alex Horne said. "This matter was discussed again during a meeting with UEFA after those disgraceful scenes which followed the final whistle.
"No football team should be asked to play in any environment where racial abuse, violence and threatening behaviour are prevalent. We must question the validity of sending a team to Serbia in the future."
Horne also stressed that "we must defend Danny Rose, who was sent off due to the frustration of being a target of racial abuse."
Rose complained that trouble had been brewing throughout the evening.
He was sent off after kicking a ball into the stands after the final whistle following apparent provocation, gesturing to the crowd that he was racially abused.
"The monkey chanting started long before I got sent off," Rose told British broadcaster Sky Sports. "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."
Rose said he complained to assistant coach Steve Wigley about problems when the team went out to warm-up before the game.
"They started the monkey chanting straight away. I asked the lads if they could hear it and they said they could hear it," Rose said. "Halfway through the warm-up I went to 'Wigs,' the assistant manager, and told him what was happening. He said I had to try my best to get through it and they would deal with it straight away after the game.
"In the first half I went down to get the ball for a throw-in and the fans started again with the monkey chants, but the first half was nowhere near as bad as the second half. In the second half I had two stones hit me on the head when I went to get the ball for a throw-in. Every time I touched the ball there was monkey chanting again."
But Serbia captain Slobodan Medojevic accused the English players of triggering the incident at the end of the game.
"My teammates told me they were provoked by the gestures of the English players toward our fans at the stadium," he said. "I don't think it's only our fault for the incidents, but also of the English players ... even if there were such chants, they could have been made by maximum five or six people."
Associated Press writers David Stringer in London and Dusan Stojanovic in Belgrade, Serbia, contributed to this report.