UK Prime Minster Boris Johnson said fans who racially abused black England players should 'crawl back under a rock'.
High profile figures including the Duke of Cambridge have led a chorus of condemnation at the abuse aimed at three players on the England football team following their defeat in the Euro 2020 final.
Marcus Rashford, Jadon Sancho and Bukayo Saka were singled out on social media after all three players missed penalties in the 3-2 shootout loss against Italy.
"For those who have been directing racist abuse at some of the players, I say 'Shame on you'," Johnson said in a Downing Street press briefing on Monday. "And I hope you will crawl back under the rock from which you emerged.
London’s Metropolitan Police said it was investigating “offensive and racist” messages on social media.
Prince William, who is president of the Football Association and watched Sunday's final at Wembley, said he was "sickened by the racist abuse aimed at England players after last night’s match".
"It is totally unacceptable that players have to endure this abhorrent behaviour," he said.
"It must stop now and all those involved should be held accountable."
England manager Gareth Southgate said the racist abuse directed at players was "unforgiveable".
"It's just not what we stand for," he said.
"We have been a beacon of light in bringing people together in people being able to relate to the national team, and the national team stands for everybody, and so that togetherness has to continue. We have shown the power our country has when it does come together and has that energy and positivity together."
In Rashford's home town in Manchester, a mural in his honour was defaced with offensive graffiti within hours of his missed penalty.
Greater Manchester Police said they were called at 2.50am on Monday to reports of the racially aggravated damage to the mural.
"This is disgraceful behaviour and will absolutely not be tolerated," Chief Superintendent Paul Savill said.
The FA urged the government to introduce new legislation to clamp down on online abuse.
“We could not be clearer that anyone behind such disgusting behaviour is not welcome in following the team. We will do all we can to support the players affected while urging the toughest punishments possible for anyone responsible," it said.
“We will continue to do everything we can to stamp discrimination out of the game, but we implore government to act quickly and bring in the appropriate legislation so this abuse has real-life consequences.
“Social media companies need to step up and take accountability and action to ban abusers from their platforms, gather evidence that can lead to prosecution and support making their platforms free from this type of abhorrent abuse.”
England’s players have taken the knee before games at the Euros to highlight the fight against racial inequality.
Rashford, who plays for Manchester United, noted the racial abuse he received on social media in May after the team lost the Europa League final.
Southgate was criticised for his strategy of bringing in Rashford and Sancho off the bench to take penalties while star Raheem Sterling was sidelined in the shootout.
“They were the best takers we had left on the pitch,” he said.
“We win and lose together.”
Nineteen police officers were injured as they confronted "volatile crowds" after fans clashed with each other and officials near Wembley stadium.
A total of 49 people were arrested were arrested for a "variety of offences", police said.
The force gave no detail to the extent of the officers' injuries but said the behaviour of some fans had been "wholly unacceptable".
The Metropolitan Police Federation, which represents thousands of London police officers, said "these people should be ashamed of themselves".
"They are not fans. They are thugs. We wish our injured colleagues well," it said.
Before the game, dozens of ticketless fans were able to break into the stadium.
FA chief executive Mark Bullingham apologised to affected fans and said the security team had "never seen anything like it".
"We have got a fantastic security team at the stadium and they have never seen anything like it," he told BBC's Radio 4 Today programme.
"There were a large number of drunken yobs trying to force their way in, we run a stadium not a fortress."
Earlier, fans were pictured in London's Leicester Square throwing bottles and road cones, leaving the area littered with rubbish.
About 60,000 fans at Wembley witnessed the Three Lions' defeat, while millions watched in fan zones and homes across the country.
The Cambridges described Sunday's result as "heartbreaking".
"Heartbreaking. Congratulations Azzurri on a great victory," the royal couple wrote on Twitter.
"England, you've all come so far, but sadly this time it wasn't our day. You can all hold your heads high, and be so proud of yourselves - I know there's more to come."
Harry Kane, the England captain, said the defeat would "hurt for the rest of our careers".
"We should be extremely proud as a group of what we have achieved," he said.
"I couldn't have given more, the boys couldn't have given more. Penalties is the worst feeling in the world when you lose. It wasn't our night but it's been a fantastic tournament and we should hold our heads high."