England manager Gareth Southgate said the racist abuse aimed at Marcus Rashford, Jadon Sancho and Bukayo Saka after the Euro 2020 final defeat by Italy was “unforgivable”.
Prime Minister Boris Johnson and the Football Association also condemned it.
All three players missed penalties in the 3-2 shootout loss and were targeted on social media after the game.
The Metropolitan Police is investigating the abuse and said “it will not be tolerated”.
“It’s just not what we stand for,” said Southgate.
“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.
“It’s my decision who takes the penalties, it’s not a case of players not volunteering or more experienced players backing out.”
England and Borussia Dortmund midfielder Jude Bellingham tweeted a picture of the three players wearing crowns and wrote: “We win together and we lose together. So proud to have team-mates with such top character. As for the racism, hurtful but not surprising. Will never get bored of saying that more needs to be done. Educate and control the platforms.”
European football’s governing body Uefa condemned the “disgusting racist abuse”, adding: “We stand by the players and the FA’s call for the strongest possible punishments.”
On Monday, League Two side Leyton Orient said they had banned a fan for three years in connection with the abuse.
“The supporter in question’s actions on Twitter were alerted to the club late last night, and action has been taken swiftly to issue a banning order,” the club said.
England had reached their first final in a major tournament since winning the World Cup in 1966 and, despite taking the lead against Italy, drew 1-1 after extra time before a penalty shootout.
“This England team deserve to be lauded as heroes, not racially abused on social media,” said the prime minister.
“Those responsible for this appalling abuse should be ashamed of themselves.”
England’s players have taken a knee before games at the Euros to highlight the fight against racial inequality.
On the day the tournament started on 11 June, the prime minister did not condemn fans who jeered when England players took the knee during two warm-up games.
Instead, Johnson said he wanted to see fans “getting behind the team to cheer them on” – and was then accused of not having “the guts to call it out” by Labour leader Sir Keir Starmer.
We implore government to act quickly – FA
The FA said it was “appalled” by the “online racism” directed at the three players following the defeat at Wembley.
It added: “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.
“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.”
In February, the government threatened social media companies with “large fines” if they failed to tackle abuse on their platforms.
“It’s unbelievable that we are still talking about it,” FA chief executive Mark Bullingham told BBC Sport. “We’ve been so clear, these social media companies need to act. They need to stamp it out and they can do that. “We are reiterating a call for the government to bring in the Online Harms Bill as soon as they can. We don’t think it’s acceptable in any walk of life for this racist abuse to happen and we want it to stop.”
Rashford highlighted racial abuse he received on social media in May after losing the Europa League final with Manchester United.
And last year Sancho was among sport stars protesting against racism following the murder of George Floyd by a police officer in Minneapolis.
Social media companies have been criticized for a perceived lack of action on racist abuse on their platforms, and in April Instagram announced a tool to enable users to automatically filter out abusive messages from those they do not follow.
Following numerous instances of online abuse, a number of clubs, players, athletes and sporting bodies took part in a four-day boycott of social media in April to encourage companies to take a stronger stance against racist and sexist abuse.
On the back of the abuse suffered by England’s players after the Euro 2020 final, Facebook said it had recently announced tougher measures on its Instagram platform, including permanently deleting accounts that repeatedly send abusive direct messages.
“No one should have to experience racist abuse anywhere, and we don’t want it on Instagram,” said a Facebook spokesperson.
“We quickly removed comments and accounts directing abuse at England’s footballers last night and we’ll continue to take action against those that break our rules.
“In addition to our work to remove this content, we encourage all players to turn on Hidden Words, a tool which means no one has to see abuse in their comments or DMs.
“No one thing will fix this challenge overnight, but we’re committed to keeping our community safe from abuse.”
Twitter said it had removed more than 1,000 posts over the past 24 hours and suspended a number of accounts for violating its rules.
Southgate said his team would “heal together as a team now” and that “we’re there for them [Sancho, Rashford and Saka] and I know that 99% of the public will be as well”.
He added: “Bukayo in particular has been an absolute star in this tournament, incredible maturity and the way he has played has brought a smile to so many people’s faces.
“He’s become such a popular member of the group and I know he has got everybody’s support.”
The Professional Footballers’ Association joined the condemnation, saying those responsible “represent the worst of us”, and that the response from social media companies was “insufficient”.
“Racist abuse causes trauma. It will impact the targeted players, their team-mates, and we know it will also affect their peers,” the PFA said.
“It causes hurt to all the other fans who view online hate, and it will inevitably live with the next aspiring generation of young players.”