Mr Hancock replied: "Well, because, the reason that I'm glad now is because we've been able to sort that out now and put that into place so that's good."
Co-presenter Susanna Reid chimed in: "No thanks to you."
Morgan said: "Let's be honest, you got shamed into it by a football player. A young football player with a conscience who managed to prick the conscience of you and the government."
Footballer Marcus Rashford brought the issue into the spotlight, raising concerns online over the quality of food given to children as part of a school meal voucher scheme.
You can watch the full exchange in the video player at the top of the article.
On Twitter, Morgan said he'd "never had a reaction to any interview clip quite like this one", racking up tens of thousands of likes with thousands of others reacting to the answer evasion.
Comedian Alistair Green jumped on the awkward exchange, and his skit has also gone viral.
Manchester United forward Rashford campaigned in 2020 for free meals to be provided to disadvantaged children during the school holidays.
He was awarded an MBE (Member of the British Empire) in the Queens's birthday honours for his work to address child poverty, including raising £20 million (NZ$37.9 million).
But more recently, Rashford has raised concerns about the quality of the food parcels being handed out to families claiming their school meal vouchers.
He shared photos online of the dismal deliveries being dropped to students in lockdown who would normally qualify for free meals at school.
"Just not good enough," he said on Twitter.
One mother posted an image of her $55 delivery expected to last for 10 days.
The photos included potatoes, cans of beans, a loaf of bread and bottles of water.
Rashford sought a meeting with UK Prime Minister Boris Johnson over the issue.
Johnson said the parcels from contracted firm Chartwells "do not meet the standards" set out by the government, labelling it "disgraceful".
"The company concerned has rightly apologised and agreed to reimburse those affected," he said.
Education Secretary Gavin Williamson said he was "absolutely disgusted" by the quality.
"As a dad myself, I just sort of thought how could a family in receipt of that really be expected to deliver five nutritious meals as is required? It's just not acceptable," he said.
