More than 1,000 schools in America's second-biggest city were searched on Tuesday after classes were cancelled.
Officials in New York, the biggest city, said they had received a similar threat but had ignored it as a hoax.
Los Angeles police chief Charlie Beck said it was "very easy in hindsight to criticise the decision".
"We have suffered too many school shootings in America to ignore these kinds of threats," he added.
In New York, police commissioner William Bratton and federal officials who asked not to be identified described the decision in Los Angeles as an "overreaction", Reuters news agency reports.
New York Mayor Bill de Blasio had concluded the threat contained "nothing credible".
Schools in Los Angeles are preparing to reopen after being shut down over an email threat, in a move queried by police officials in New York.