MPs from Shropshire and Telford & Wrekin were among those to have resisted demands led by footballer Marcus Rashford to extend free meals into the school holidays during the coronavirus pandemic.
But chairman of the Liaison Committee and Harwich and North Essex MP Bernard Jenkin said: "I think we have to admit that we have misunderstood the mood of the country here."
Telford MP Lucy Allan said Government funding had already been provided to local authorities to help with the response to the coronavirus pandemic, and that the vote was over which aid works better.
Ms Allan said: "The government has been providing additional funding to Telford & Wrekin to assist our local response to the current crisis.
"The government specifically provided all councils with ring-fenced funding for food and essential supplies for those most in need.
"In addition, a further £4.8 million has just been allocated to Telford & Wrekin Council to assist in our local coronavirus response.
"This funding is discretionary and can be spent where councillors consider it is needed most. Councils across the country have been providing food aid to residents using Government funding, as we have in Telford, and this is very welcome and has been very effective.
"The question MPs debated was whether giving money to local councils for local food aid initiatives works better than giving families vouchers to redeem in supermarkets. MPs have different views on this but are united in working to ensure our constituents can access food and essential supplies at this very difficult time. I support the local initiatives taking place in Telford to help our community through this crisis.
"I urge any family in need to contact my office in Telford, where my full-time team are working tirelessly to ensure my constituents get the help they need."
Wrekin MP Mark Pritchard highlighted that Universal Credit and the minimum wage had been increased.
Mr Pritchard said: "There will always be a place for free school meals for those on the lowest incomes or children who need such support, but the free school meals funding is not infinite given so many other financial demands across all age ranges since the pandemic started."
Wednesday's vote on Labour's motion to extend free school meals over the holidays saw 261 in favour and 322 against.
On Thursday, Ludlow MP Philip Dunne said it was an opposition day debate meant to "embarrass" the government.
Mr Dunne said: "On the subject of the issue the government has provided very significant support to households during lockdown, including free school meals during holidays and they are continuing to provide increased support to low income households through the £20 a week Universal Credit uplift, uplift to those on housing benefit and help with council tax and those measures continue, and of course in areas like Shropshire, where most people continue in work – although unemployment is rising – those people in work should be able to take responsibility for their family during half term."
Shrewsbury & Atcham MP Daniel Kawczynski added: "The government has put an extra £9 billion into social security to help the poorest families.
"Bearing in mind the huge support that I am very pleased we are putting into Universal Credit and social security, designed to help the poorest families, I am very proud of that and I stand by that."