His remark drew applause from spectators in the room.
Across the Capitol, the House Education and Workforce Committee planned to hear from school safety experts and counselors about how to keep students safe.
"How can we be confident that something like this does not happen again?" asked John Kline, R-Minn., the Republican panel's chairman as the meeting began.
His Democratic counterpart, Rep. George Miller of California, said school safety is linked to firearms.
"Sandy Hook is an event that calls us on us as policymakers to do something. ... A school must be a place where children feel secure," Miller said. "Turning schools into armed fortresses is not the answer."
Instead, he said schools need to add counseling services and mental health programs.
In their prepared testimony, witnesses there were careful not to endorse the NRA's suggestion that armed volunteers in schools were a realistic answer to prevent future attacks.
"I cannot emphasize enough how critical it is for officers to be properly selected and properly trained to function in the school environment," said Mo Canady, executive director of the National Association of School Resource Officers.
Despite the raw emotion, Feinstein's effort to ban assault weapons is expected to fall short due to opposition by the National Rifle Association and many Republicans, plus wariness by moderate Democrats.
Feinstein's bill has attracted 21 co-sponsors, all Democrats. Including herself, it is sponsored by eight of the 10 Judiciary panel Democrats — precarious for a committee where Democrats outnumber Republicans 10-8. Democrats on the panel who haven't co-sponsored the measure include the chairman, Pat Leahy of Vermont, who said Monday he hadn't seen the bill.
Obama made bans on assault weapons and large capacity magazines key parts of the gun curbs he proposed in January in response to the Connecticut school massacre.