Hancock warned that the strict measures could stay in place until the virus vaccine is fully rolled out.
"We acted very quickly and decisively," Hancock told Sky News, justifying the "stay at home" order and closure of non-essential shops affecting around a third of England's population.
"Unfortunately the new strain was out of control. We have got to get it under control."
Prime Minister Boris Johnson announced on Saturday that millions must cancel Christmas plans and stay home because the new strain was spreading far more quickly.
Hancock told Sky News that the situation was "deadly serious."
"It's going to be very difficult to keep it under control until we have the vaccine rolled out," he said, adding: "This is what we face over the next couple of months."
It emerged that scientists first discovered the new variant in a patient in September.
Susan Hopkins of Public Health England told Sky News that the agency notified the government on Friday when modelling revealed the full seriousness of the new strain.
She confirmed the figure given by Johnson that the new virus strain could be 70 percent more transmissible while saying this was an initial figure.
"I think 70 percent looks like a good number to land on at the moment," she said.
Like last year's stampede to grab a share of facial masks and protective clothes, the scramble for Covid vaccines is heating...