In the coming weeks, the inquiry is due to hear about the difference in opinion between the former education secretary Gavin Williamson and Boris Johnson about the closing of schools in January 2021.
Baroness Longfield said the 2021 closure would have been avoidable with better planning, but says the government did not use the time over the previous summer to prepare for a future lockdown.
On Monday, Galina Ward KC, for the DfE, said there was "a really difficult balance to be struck between trying to keep [schools] open at all costs, or having targeted early closures to avoid longer ones later, but then potentially closing schools at a time when it may become apparent with hindsight that it wasn't in fact necessary".
"There simply are no easy answers and we look forward to all of the complexities being fully ventilated in this module," she said.
Although vulnerable children were allowed to attend schools in the first lockdown, only 5% attended in the first few weeks, the inquiry was told.
Baroness Longfield said the "stay at home" message from government seemed to show that ministers hadn't understood the complexity of life for a lot of children and families, with the message being that it was "unsafe to leave your house".
"It meant that those families with vulnerable children who might have attended wondered why their children might take the risk to attend school when everyone else wouldn't," she said.
The policy was a good decision and well-intentioned, she told the inquiry, but because of how it was communicated, it was almost seen as a punishment, rather than an offer from government to help families.