The Manchester United and England striker was furious after a Labour Party motion to extend the scheme was defeated in the Commons last night by a majority of 61.
He said the move meant children would be "going to bed tonight not only hungry but feeling like they do not matter", and accused MPs of allowing their views to be "clouded by political affiliation".
Labour had called for 1.4 million disadvantaged children to be handed £15-a-week food vouchers over each holiday up to Easter 2021, and accused the Tories of voting to let children "go hungry".
Earlier this year Rashford ran a successful campaign for the provision of food vouchers over the six-week summer holidays after schools had been shut down due to the pandemic. The scheme is believed to have cost around £126m.
Education Secretary Gavin Williamson, the MP for South Staffordshire, said it was right to provide free school meals during holidays during the "unprecedented and unpredictable period" at the start of the pandemic.
"But we are in a different position now that we have welcomed all pupils back to school," he added.
"Taken together it is clear that the Government has taken very significant and unprecedented action to support children and families at risk of hardship during this period.
"Free school meals are and always have been about supporting children with a meal to help them when they’re at school or currently at home learning.
"But it is our support through Universal Credit and our comprehensive welfare system that supports families."
Suzanne Webb, the Conservative MP for Stourbridge, said she voted against the motion because it was "just one more action by those intent on undermining and derailing the response to this national crisis with yet another strapline".
She said: "This is a Government who have during this crisis delivered an unprecedented set of measures to ensure that no child was left behind while schools were closed – a Government who will always provide a safety net, and not just at a time of national crisis, to ensure that those who need it most are supported unquestionably."
Walsall South MP Valerie Vaz, the Shadow Leader of the Commons, said: "The Government has abdicated its responsibility to stop children going hungry this winter.
"No child should go hungry over the holidays, especially when many families are facing redundancies and lengthy periods in lockdown.
"In Walsall South, there are over 5,000 children will be affected by the Government’s decision to vote down the provision of free school meals.
"Once again, they are failing to provide my constituents with the financial support they urgently need.
"I pay tribute to Marcus Rashford and all who have campaigned on this important issue. I will continue the campaign to prevent needless child hunger this winter and the Government must reconsider."
Linda Leach, a Labour councillor in Wolverhampton and the Cabinet member for adults, said she was appalled that the city's Tory MPs had voted to "deprive our children".
"Some people just don’t understand the poverty and the hardships some parents have to endure," the Bilston North councillor said.
"It’s not the child’s fault that they don’t have a hot meal at home after school. No child should go hungry in this day and age."
Stuart Anderson, the Tory MP for Wolverhampton South West, said he opposed the motion as it was "the role of the wider welfare system to help families that require extra support" outside school term.
He pointed out that the Government had announced an extra £6.1m funding for the city council and that Universal Credit and Working Tax Credit had been uplifted by around £1,000 a year for the next 12 months.
"We must also seek to address the issues which fuel demand for free school meals," he added.
"To do this, the Government has started an independent and comprehensive review of our entire food system.
"The National Food Strategy will publish sustainable, long-term recommendations that will help the Government to tackle some of the most significant challenges to improving the health of our nation.
"I am confident that ministers will carefully consider these recommendations, and I will closely monitor progress made."
Following the vote, Rashford, who was awarded an MBE for his campaign, said: "We must stop stigmatising, judging and pointing fingers. Our views are being clouded by political affiliation.
"This is not politics, this is humanity."
Tory MPs were under orders to vote against the plan, with Boris Johnson saying it was not the job of schools to "regularly provide food during the school holidays".
Five Conservative MPs rebelled against their party by voting with Labour, including Caroline Ansell who has subsequently quit her role as a parliamentary private secretary.