The England star had been campaigning to extend free school meals over the half term holidays and launched a petition urging the government to make a change.
However, MPs controversially voted down his bid with only five Conservatives rebelled against the government to vote for feeding more than £1.4 million children during school breaks until Easter next year.
The bid, tabled by Labour, was defeated by 261 votes to 322.
Following the failed vote, Rashford told politicians to “stop stigmatising, judging and pointing fingers” as he warned a “significant number” of children will go to bed hungry and “feeling like they do not matter”.
Sheffield pub, The Handsworth Inn, took to social media to inform its customers that they would be putting together packed lunches to help ‘take some stress away from struggling parents.
In the Facebook post, the owners said: “If you need a packed lunch or know someone who this might benefit please send us a private message and let us know what days and how many packed lunches you need.
"If anyone would like to help by donating a pack of ham, bread cakes or a bag of fruit we’re more than happy for you to drop off at the pub.
"These will be free of charge, we just want to help out the best we can.”
The pub’s inspirational post has been shared far and wide and has even been shared on Twitter by Rashford himself.
Downing Street ruled out performing a late U-turn ahead of the vote, with Prime Minister Boris Johnson telling MPs that support will continue for children on low incomes.
“We will continue to use the benefits system and all the systems of income to support children throughout the holidays as well,” he added.
Culture Secretary Oliver Dowden claimed the Government had not ignored Rashford on the issue.
He told ITV’s Peston: “Well, we are certainly not ignoring Marcus Rashford, and I pay tribute to the work he has done.
“It is a fantastic example – as a minister for culture and sport – seeing sportspeople playing such a leading role in the national debate.
“And we are committed to free school meals.”