A mural in Rashford’s home town of Withington, Manchester, was also defaced with offensive graffiti, before fans covered it in supportive messages.
Marcus Rashford has said he is "overwhelmed" and "lost for words" as he thanked supporters who posted messages of support on a mural depicting the England striker.
Earlier, England footballer Tyrone Mings criticised UK Home Secretary Priti Patel for "stoking the fire" of racism in previous comments when she described players taking the knee as "gesture politics".
Ms Patel was among senior political figures who condemned the abuse the players received.
“It has no place in our country and I back the police to hold those responsible accountable,” she said on Twitter.
In a reply to the tweet, Mings said Ms Patel was “pretending to be disgusted” after she previously criticised players for taking the knee to protest against racism and suggested supporters could choose to boo players who participated.
"You don’t get to stoke the fire at the beginning of the tournament by labelling our anti-racism message as ‘gesture politics’ and then pretend to be disgusted when the very thing we’re campaigning against, happens," Mings said.
Asked before the tournament about players who took the knee in a symbolic gesture against racism, Ms Patel told broadcaster GB News: “I just don’t support people participating in that type of gesture, gesture politics, to a certain extent, as well.”
Ms Patel declined to comment on Mings’ tweet.
But Conservative MP and former UK defence minister Johnny Mercer said he supported the footballer’s view.
“The painful truth is that this guy is completely right. Very uncomfortable with the position we Conservatives are needlessly forcing ourselves into,” he said.
“Do I fight it or stay silent? Modern Conservatism was always so much more to me. We must not lose our way.”
Conservative peer Sayeeda Warsi also accused her party of “dog whistling” and said all members needed to "think about our role in feeding this culture in our country".
“It’s time to stop the culture wars that are feeding division,” she said.
“Dog whistles win votes but destroy nations.”
The opposition Labour Party said Prime Minister Boris Johnson and Ms Patel were guilty of hypocrisy.
"The prime minister failed to call out the booing so whatever he says today rings hollow," Labour leader Sir Keir Starmer said.
The Prime Minister on Tuesday was reportedly preparing to hold talks about online abuse with companies including Facebook, Twitter and Instagram in No 10.
“He said the abuse was utterly disgraceful and had emerged from the dark spaces of the internet,” the Prime Minister’s official spokesman said.
“He said he would use today’s meeting with social media firms to reiterate the urgent need for action ahead of tougher laws coming into force through the Online Harms Bill.”
An online petition has been signed by thousands of people demanding that racists who abuse players be barred from English football for life.
By Tuesday morning, the petition, set up by a group called The Three Hijabis, had gained about 700,000 signatures having set an initial target of 500,000.
Amna, a member of the group, said "words alone" were not enough to tackle racism.
"Those perpetrating this behaviour need to be held accountable, and we hope that the FA will respond to this petition and start to address this issue with actions, not just words," she told The National.
Chief Secretary for the Treasury Steve Barclay said on Tuesday that Ms Patel understood racism.
“The home secretary herself has been the subject of appalling online racist abuse,” he told Sky News.
“She has consistently taken action against the extreme right wing groups who are responsible for this.”
Rashford apologised for his penalty miss but said he "will never apologise for who I am".
"I can take criticism of my performance all day long, my penalty was not good enough, it should have gone in, but I will never apologise for who I am and where I came from,” he said.
"I've felt no prouder moment than wearing those three lions on my chest and seeing my family cheer me on in a crowd of tens of thousands."
On Monday, Mr Johnson said fans who racially abused black England players should “crawl back under a rock”.
"For those who have been directing racist abuse at some of the players, I say, 'Shame on you'," he said.
"And I hope you will crawl back under the rock from which you emerged.”
London’s Metropolitan Police said it was investigating “offensive and racist” messages on social media.
Prince William, president of the Football Association, attended Sunday's final at Wembley. He said he was "sickened by the racist abuse aimed at England players after last night’s match".
"It is totally unacceptable that players have to endure this abhorrent behaviour," he said.
"It must stop now and all those involved should be held accountable."