Prime Minister David Cameron was "appalled" by the ugly scenes at the end of the England Under-21 football team's match against Serbia.
The Government is giving its full backing to a Football Association complaint over alleged racist taunts and sport minister Hugh Robertson has written to Uefa president Michel Platini urging an investigation, the Prime Minister's official spokesman said.
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 player Danny Rose complained of racist abuse, including monkey chants, during during the Euro 2013 play-off in Serbian city Krusevac, and said he was also hit by missiles thrown from the crowd.
The Tottenham defender, on loan at Sunderland, was sent off after the final whistle for kicking a ball in anger as scuffles broke out involving Serbian supporters, players and officials.
In his letter to Mr Platini, Mr Robertson called for tough sanctions from the governing body.
The minister said: "The scenes at the end of the game last night 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."