Feinstein, the chairwoman of the Senate Intelligence Committee, said on the "Fox News Sunday" program that Petraeus' resignation on Friday "was like a lightning bolt."
She said there will be an investigation into why the FBI failed to inform her and others on the intelligence committee before Friday about the extramarital affair between Petraeus and his biographer, Paula Broadwell, when the FBI probe had been proceeding for weeks.
The California Democrat said there was no connection between Petraeus' resignation and the September 11, 2012, killings in Benghazi. Petraeus had been scheduled to testify about the Benghazi case on Thursday in a closed session of the committee; Mike Morrell, the acting CIA director, is now expected to do so.
She said the committee may decide to call Petraeus in a future meeting of the intelligence panel on the Benghazi killings. Four U.S. citizens were killed, including Ambassador Christopher Stevens.
"My biggest concern is, there are literally hundreds of threat warnings in the material that has been accumulated," Feinstein said. "There were five attacks during the year, one prior attack on the consulate itself. The question I have is ... why wasn't something done about it?"
U.S. Representative Peter King, the Republican chairman of the House Homeland Security Committee, raised questions about why it took FBI investigators so long to inform President Barack Obama and others in his administration that Petraeus was involved.
FBI TIMELINE QUESTIONED
"The timeline has to be looked at and analyzed," the New York congressman said on CNN's "State of the Union. "Because obviously this was a matter involving a potential compromise of security and the president should have been told about it at the earliest stage."
Republican Senator Lindsey Graham said he was ready to turn the page on the scandal that prompted Petraeus to resign, but said the former general must testify before Congress about what he called a "national security failure" at Benghazi.
Graham, of South Carolina, called for a Watergate-style joint select committee of members of the House and Senate to investigate the matter.
Speaking on "Face the Nation" on CBS, Graham said the Pentagon and the U.S. intelligence community have much to explain in this case, but singled out Susan Rice, the U.S. ambassador to the United Nations, for her role.
"I don't, quite frankly, trust her rendition of Benghazi," Graham said. Rice initially described the attack as a spontaneous outburst rather than a planned attack. Her handling of the matter provided fodder to Republican opponents in the final months of Obama's re-election campaign.
Rice has been mentioned as a possible choice by Obama to succeed Secretary of State Hillary Clinton, but Graham said Rice's nomination to this post "would have incredibly difficult time getting through the Senate."
"I would not vote for her unless there's a tremendous opening up of information explaining herself in a way she has not yet done," Graham said of Rice.