UK Prime Minister David Cameron was "appalled" by the ugly scenes at the end of the England Under-21 match against Serbia, Downing Street said.
The PM's official spokesman said the government was giving its full backing to a Football Association complaint over alleged racist comments by Serbian supporters, and sport minister Hugh Robertson had written to UEFA president Michel Platini urging an investigation.
Britain expects "tough sanctions" if racism is proved, the spokesman said.
Commenting on Mr Cameron's response, the spokesman said: "He was appalled by the scenes that we have seen in Serbia.
"We are determined to stamp out racism internationally and at home and we are giving our full backing to the FA's complaint on this issue.
"Clearly it is for UEFA to investigate this issue but we would expect tough sanctions. If we are going to stamp out racism from football then it is no good giving derisory fines, as have been handed out in the past.
"It is not good enough to say that people should shake hands and forget about it."
England Under-21 defender Danny Rose wants Serbia to be banned after he complained of racist abuse and being hit by missiles in Krusevac.
The Tottenham man, currently on loan at Sunderland, said he had been subjected to monkey taunts long before the violent scenes which marred the end of the Euro 2013 play-off.
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."
Robertson has given his full support to the Football Association, who reported a number of incidents of racism to UEFA.
The minister said: "The scenes at the end of the game were disgraceful. I have written to UEFA president Michel Platini, in support of the FA, urging them to investigate immediately.
"Racism in any form is unacceptable and must be stamped out. We would expect tough sanctions from UEFA on anyone found guilty of racist abuse."
England assistant coach Steve Wigley was caught up in the trouble and was manhandled as he made his way to the tunnel after the game.
Rose said the issues were a culmination of problems which had been brewing throughout the evening at the Mladost Stadium.
The 22-year-old added: "It started when we went out for the warm-up.
"They started the monkey chanting straight away. I asked the lads if they could hear it and they said they could hear it.
"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.
"After 60 minutes my mind wasn't really on the game after that. I was just so angry and it was just so hard to concentrate.
"I could have cost the lads the game because I made a few mistakes through not concentrating.
"Then obviously we scored. After 90 minutes' worth of abuse I just expressed my emotions as soon as we scored.
"Then the next thing I know all the Serbia players have run over and were all surrounding me, pushing me and a brawl broke out."
Connor Wickham's injury-time strike clinched a 2-0 aggregate success.
