James Comey's announcement of a new inquiry into her use of email while secretary of state shortly before election day had stopped her campaign's momentum, Mrs Clinton said.
The Democratic candidate was speaking to top party donors in a phone call, which was leaked to the media.
Protests are continuing against the victory of her rival, Donald Trump.
In New York, about 2,000 marchers headed for the skyscraper where the president-elect lives, shouting "not my president".
Anti-Trump activists have held daily protests in US cities since his election victory was confirmed on Wednesday.
Mr Trump seems to be rowing back on some of his campaign pledges. Having promised to scrap President Barack Obama's healthcare law dubbed "Obamacare", he now says he is open to leaving intact key parts of the act.
Asked by the Wall Street Journal whether he would implement a promise to appoint a special prosecutor to investigate Mrs Clinton's use of a private email server while secretary of state, he listed healthcare, jobs, border control and tax reform as greater priorities.
The Republican is due to be sworn in on 20 January, taking over from Mr Obama, who will have completed two terms in office.
Mrs Clinton, who served as Mr Obama's secretary of state from 2009 to 2013, has been keeping a low profile since conceding victory.
On 28 October, Mr Comey informed Congress that the FBI was examining newly discovered emails sent or received by Mrs Clinton, thus reviving an investigation which had been completed in July.
Then, on 6 November, two days before the election, Mr Comey announced in a second letter that he was standing by his original assessment - that Mrs Clinton should not face criminal charges.
"There are lots of reasons why an election like this is not successful," Mrs Clinton told the donors on a farewell conference call on Saturday.
"But our analysis is that Comey's letter raising doubts that were groundless, baseless, proven to be, stopped our momentum. We dropped, and we had to keep really pushing ahead to regain our advantage."
According to US media, she added that Mr Comey's later recommendation that she should face no charges had energised Mr Trump's supporters.
Her campaign team said that despite Mrs Clinton being cleared of criminal behaviour, the move only revived Mr Trump's claim that the Democratic candidate was being protected by a rigged system.
Despair and anger
The New York marchers rallied in Union Square Park for the march to Trump Tower, from which the next president has been planning the transition to his inauguration.
One organiser of the New York protest, Kenneth Shelton, told the BBC that it was not an attempt to challenge the legitimacy of Tuesday's election. "We lost," he admitted.
Placards at the demonstration express despair and anger, the BBC's Paul Adams says.
One read "Trump: An American Tragedy" while the message on another read "Now We're Your Nightmare".
"We must unite despite our differences to stop HATE from ruling the land," organisers of the New York protest wrote on Facebook. Demonstrations in the city earlier this week drew thousands of people.
Demonstrations are also scheduled for Saturday in Los Angeles and Chicago.
On Friday demonstrations in Portland, Oregon, turned violent and one person was shot but most rallies have passed off peacefully.