ITV News Correspondent Libby Wiener reports on the pressure the government and social media companies are feeling over racism in football
The 21-year-old sent a message of support to other young people who have received similar abuse.
Sancho, Rashford and Saka were the three players who missed penalties in the 3-2 shootout against Italy on Sunday.
Soon after England's defeat, the players became the targets of racist abuse on social media.
Sancho wrote in an Instagram post on Wednesday: "I’m not going pretend that I didn’t see the racial abuse that me and my brothers Marcus and Bukayo received after the game, but sadly it's nothing new.
"As a society we need to do better, and hold these people accountable.
"Hate will never win. To all the young people who have received similar abuse, hold your heads up high and keep chasing the dream."
He continued: "I want to say a massive thank you for all the positive messages and love and support that far outweighed the negative.
"It’s been an honour as always representing England and wearing the Three Lions shirt, and I have no doubt we’ll be back even stronger! Stay safe & see you soon."
Sancho’s and Saka's spot-kicks were saved by Italian goalkeeper Gianluigi Donnarumma, while Rashford hit the post. Italy was handed a 3-2 shoot-out victory after the game had finished 1-1 following extra-time.
The midfielder said: “I’ve had a couple of days to reflect on Sunday's final and still feel a mix of emotions. I would like to say sorry to all my teammates, coaching staff and most of all the fans who I let down.
"This is by far the worst feeling I’ve felt in my career.
"It’s hard to even put into words the real feeling, but there were so many positives to take away from this tournament though the defeat will hurt for a long time."
He continued: "I was ready and confident to take it, these are the moment's you dream of as a kid, it is why I play football. These are the pressured situations you want to be under as a footballer.
"I’ve scored penalties before at club level, I’ve practiced them countless times for both club and country so I picked my corner but it just wasn’t meant to be this time."
After calls by more than a million people to ban racists from football games, Prime Minister Boris Johnson announced on Wednesday that the football banning order regime will be changing to cover online racism.
Harry Kane previously told those who send abuse on social media: "You're not England fans and we don't want you."
The England captain tweeted on Monday: "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."
On Monday, prime minister Mr Johnson told said racist abusers to "crawl back under a rock".
"To those who have been directing racist abuse at some of the players, I say: shame on you, and I hope you will crawl back under the rock from which you emerged."