England forward Rashford, who has been awarded MBE for his work in tackling child poverty amid the COVID-19 pandemic, forced a government U-turn in July when he won his battle to ensure free meals during school summer holidays.
The 22-year-old last week proposed extending the campaign for families receiving financial assistance from the UK government into half-terms and the Christmas holidays. A petition he launched has been signed by more than 300,000 people.
The Labour Party had urged Conservative MPs to back the proposals, which could see an additional 1.5 million children aged between seven and 16 receive extra support out of term time.
But MPs voted 322 to 261 against the Labour motion which would have extended free school meals over the holidays until Easter 2021.
Following the vote, Rashford urged politicians to unite and protect the most vulnerable families and vowed to continue his campaign.
"A significant number of children are going to bed tonight not only hungry but feeling like they do not matter because of comments that have been made today," he said on Twitter.
"We must stop stigmatising, judging and pointing fingers -- our views are being clouded by political affiliation.
"These children are the future of this country. They are not just another statistic. And for as long as they don't have a voice, they will have mine. You have my word on that."
Earlier on Wednesday, Conservative MP Robert Halfon, chairman of the Commons Education Select Committee, called on the government to back Rashford's campaign and continue providing meals over the holidays.
In the Commons, however, Prime Minister Boris Johnson continued to resist calls for extra support.
Johnson's spokesman later told reporters: "While schools continue to play an integral role in the community, it's not for them to regularly provide food during school holidays."