The Three Lions came agonisingly close to winning a first major trophy since 1966, only to be denied by Italy via a penalty shootout.
Marcus Rashford, Jadon Sancho and Bukayo Saka failed to score from 12 yards and were targeted by racist trolls.
Gareth Southgate, Boris Johnson and the Duke of Cambridge all denounced the abuse.
Former England captain Beckham, 46, praised the team’s performance and said “they all deserve nothing but thanks and respect”.
He wrote on Instagram: “To Gareth and the boys…I know how much this will hurt but you have the pride and thanks of your country for what you have achieved and you have done it the right way.
“Anyone who doesn’t support and respect each and every one of you today isn’t an England fan.
“Win or lose we stand with you .. Hold those heads high..”
Borat star Baron Cohen, who has campaigned against hateful content on social media, called on Facebook boss Mark Zuckerberg and Twitter chief executive Jack Dorsey to act.
He said: “Hey Mark Zuckerberg & Jack Dorsey — Facebook/Instagram and Twitter are spreading racist attacks on these black athletes.
“Online racism leads to real-world hate crimes.
“It’s time to rid racism from your platforms once and for all!”
Baron Cohen added the hashtag #StopHateForProfit.
Formula One world champion Lewis Hamilton, who has long campaigned against racism, said he had conflicting thoughts while watching the final moments of the match.
While he was “so proud” of the team, Hamilton admitted he was “worried” about the consequences of England’s black players missing.
He said: “The pressure to deliver is felt by every sportsperson but when you are a minority representing your country this is a layered experience.
“Success would feel like a double victory, but a miss feels like a two-fold failure when its compounded with racist abuse.
“I so badly wanted that win like all of you but for me it was for much more than winning the euros, it was a much bigger picture.
“However, the disgusting behaviour by the few, shows how much work that still needs to be done.
“I hope that this opens a conversation around acceptance.
“We must work towards a society that doesn’t require black players to prove their value or place in society only through victory.
“Ultimately everyone on the England team should be so proud of their achievement and how they represented us.”
England captain Harry Kane also shared a passionate defence of his teammates and said those abusing players are not fans of the Three Lions.
He tweeted: “Three lads who were brilliant all summer had the courage to step up & take a pen when the stakes were high.
“They deserve support & backing not the vile racist abuse they’ve had since last night.
“If you abuse anyone on social media you’re not an @England fan and we don’t want you.”
US rapper and mogul Sean “Diddy” Combs also supported the players.
“We stand with you Kings,” he wrote alongside a picture of Rashford, Sancho, Saka and Raheem Sterling. “Proud of all your efforts on and off the field and we will always support you. Continue to inspire. Love.”
He added an expletive for those sending racist abuse.
Supermodel Naomi Campbell described the racism as “disgusting”.
Addressing the players targeted, she added: “I want to let you know how proud I am of you all, as you gave your all, and don’t let the ignorant voices in .. stay on your level, dream bigger, reach higher and let that drive you .. as you are winners fulfilling your life long passion.”
Campbell added the hashtags #StopTheHate and #StopRacism.
Spider-Man actor Tom Holland described the behaviour of some England fans as “despicable” following reports not only of racist abuse but violent clashes inside Wembley.
“You are not my countrymen,” he wrote.
“These players deserve nothing but respect.
“They’ve given us so much in such a difficult time and they should be held up like kings not kicked while they are down.
“To Saka, Rashford and Sancho, you had the bravery to step up.
“You guys are three lions and all decent Englishmen are proud of you and the whole team and staff and we will support you again come the World Cup.”
Chart-topping pop group Little Mix shared a statement on Instagram.
Alongside a picture of the players who failed to score from 12 yards, as well as Sterling, the band said: “If you do not stand up against racism, you are also part of the problem.
“What these young men have had to deal with is beyond disgraceful.
“We stand with you Kings.”
Girls Aloud star Kimberley Walsh shared the same picture and said: “These young, brave men played with dignity for their country and deserve nothing but love.
“Let’s lift them up and drown out all the abhorrent racist hate.”