Boris Johnson has condemned the “appalling” racist abuse on social media directed at a number of England players after their defeat to Italy in the Euro 2020 final. The Metropolitan police have also opened an investigation into the abuse.

The prime minister tweeted his condemnation on Monday morning after the Football Association issued a statement shortly after the game finished describing “disgusting behaviour” among some fans online, and urging police to implement “the toughest punishments possible”.

Johnson wrote: “This England team deserve to be lauded as heroes, not racially abused on social media. Those responsible for this appalling abuse should be ashamed of themselves.”

The Labour MP David Lammy also criticised the racist abuse targeted at three players, Marcus Rashford, Jadon Sancho and Bukayo Saka, who failed to score their spot-kicks in the penalty shootout, resulting in a 3-2 loss to Italy at Wembley.

He wrote: “This is why we take the knee. Praying for a better future – worthy of the values, beauty and respect exemplified by every single England player.”

Saka’s club, Arsenal, expressed “sorrow” at the racist abuse the 19-year-old received and said: “The social media platforms and authorities must act to ensure this disgusting abuse to which our players are subjected on a daily basis stops now. We have processes in place internally at Arsenal to ensure our players are supported both emotionally and practically on this issue but sadly there is only so much we can do.

“Our message to Bukayo is: hold your head high, we are so very proud of you and we cannot wait to welcome you back home to Arsenal soon.”

The FA statement said: “The FA strongly condemns all forms of discrimination and is appalled by the online racism that has been aimed at some of our England players on social media.

“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.”

A Metropolitan police tweet said: “We are aware of a number of offensive and racist social media comments being directed towards footballers following the #Euro2020 final. This abuse is totally unacceptable, it will not be tolerated and it will be investigated.”

None of the players had commented at the time of writing, but the England team’s official Twitter account put out a statement.

“We’re disgusted that some of our squad – who have given everything for the shirt this summer – have been subjected to discriminatory abuse online,” it said.

The FA statement said it would “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.”

A number of high-profile Twitter users gave the players their support after the game, while Instagram has been flooded with positive comments in an effort to drown out the racist abuse.

“All the boys who put themselves forward to take a pen we are proud of you – takes a form of bravery to step up in such pressurised situations. @BukayoSaka87 @Sanchooo10 @MarcusRashford we salute you boys,” wrote the former England international Rio Ferdinand.

“The racist abuse I’ve seen targeted at these incredibly talented young players who helped take us to our first major tournament final in 55 years has been vile and disgusting,” wrote Magid Magid, a former lord mayor of Sheffield. “England wouldn’t have achieved what it did without them. They deserve all our love and support!”

The London mayor, Sadiq Khan, called on social media companies to do more to hold to account those responsible for sending online abuse. He tweeted: “There is absolutely no place for racism in football or anywhere else.”

Facebook, which owns Instagram, said it tried to remove harmful content as quickly as possible and encouraged people to use the tools it offers to block abuse. “No one thing will fix this challenge overnight, but we’re committed to keeping our community safe from abuse,” it said.

Twitter said it had proactively removed more than 1,000 posts over the past 24 hours which violated its policy and also taken swift action to permanently suspend a number of accounts.