The Public Accounts Committee report says that despite being involved in a 2016 cross-government exercise on dealing with a pandemic, the DfE had "no plan" and was "unprepared" for the challenges of Covid-19.
It says that when schools were closed to most pupils in early 2020, "the DfE set no standards for in-school or remote learning during the rest of the school year", meaning "children had very unequal experiences".
It added that the DfE is still yet to properly assess its early response in order to learn lessons for the future, and that there was "little specific detail” about how it will “build the school system back better”.
West Bromwich West MP, Shaun Bailey, who sits on the committee, said: "As someone who represents an area with some of the highest child deprivation in the country, I find this report very alarming indeed.
"The events of the past year have highlighted the stark divide between the haves and the have not’s in society, and the impact this has on an individual’s education."
He added: "What is most alarming about this report, is that there appears to be very little specific detail known about how the Department for Education plans to build the school system back better in the coming weeks and months.
"They have a duty to our children to ensure that the effects of the pandemic are not felt for years to come”.
The report said that disruption to schooling had a particularly damaging impact on children who were already facing adversity.
The proportion of vulnerable children who attended school or college remained below 11 per cent until late May 2020, and only ever reached an average of 26 per cent by the end of the summer term.
Referrals to children’s social care services fell by 15 per cent and remain 10 per cent lower year-on-year – raising concerns about ongoing ‘hidden harm’ to children.
Meanwhile there is already evidence, the report says, that the DfE’s catch-up programme to make up for lost learning may not be reaching the most disadvantaged children.
A DfE spokesperson said: “Throughout the pandemic we have acted swiftly at every turn to help minimise the impact on pupils’ education and provide extensive support for schools, colleges and early years settings.
“The department has updated and strengthened its remote education expectations as best practice has developed and schools’ capabilities have increased.
“We have invested over £2 billion into schemes to provide pupils with devices for remote education and ambitious catch-up plans with funding targeted at disadvantaged children and young people who need support the most.”