England lost the match to Italy after Marcus Rashford, Jadon Sancho and Bukayo Saka failed to score during the penalty shootout. The three players were subsequently targeted by racist trolls.
Former England captain Beckham praised the current 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..”
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.
Watch: Boris Johnson and Gareth Southgate condemn racist abuse against players
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.”
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.”
Little Mix member Leigh-Anne Pinnock, who recently fronted a documentary on race and being a Black woman in the music industry, also paid tribute to the players.
"You can live here but be quiet. You can work here but not all of you. You can speak at the table but not too loud. You can play for us but you can’t lose. Ladies and gentlemen I give you the Black British Experience. We stand with you Kings x Leigh," the post read.
BBC Breakfast's Dan Walker has also criticised the behaviour of some so-called fans.
Read more: EastEnders gives nod to Euros final
In an Instagram post he shared: "I am sure I’m not alone in feeling far more annoyed / ashamed by some of the behaviour before & after the Euros final than the result itself.
"If your first response to a saved penalty is racist abuse then stop drinking, stop watching sport & get educated. This is on all of us. Win together. Lose together."
Singer Ellie Goulding opined that those dishing out hate had "let our country down and what stand for".
She shared: "Anyone who has decided that racism and hatred is the outlet for expressing their sadness at our loss needs to take a long look at the sad sight in the mirror and reevaluate themselves. We need to learn how to accept defeat with humility and grace.
"If you dealt with last nights result with furious anger and lashed out at something or someone (domestic violence surges every time a football match ends) You need to seek real help. So SO easy for you to sit and judge these incredible athletes from a sofa or the pub."
High-profile figures to have condemned the abuse also include Boris Johnson and the Duke of Cambridge as well as England's manager Gareth Southgate.
On Monday night, Rashford apologised for missing his penalty but said the positive message he received had been "overwhelming".
With additional reporting by PA.
Watch: Kane, Maguire and Grealish all break their silence as the dust settles on Euros final