The cyber attacks - which US intelligence sources believe were approved by Vladimir Putin -- were the result of a "personal beef" the Russian leader had with her, Clinton told the gathering of fundraisers, who had given a total of about USD 1 billion to her campaign.
She attributed the Russian president's vendetta to her harsh criticism of the country's 2011 parliamentary elections, which she called "so flawed, so illegitimate that it was embarrassing," CBS News reported.
"Putin publicly blamed me for the outpouring of outrage by his own people, and that is the direct line between what he said back then and what he did in this election," she said, according to audio obtained by the New York Times adding "he is determined to score a point against me which he did. But also undermine our democracy".
That Putin's grudge against Clinton led to Russia's involvement in the US elections was a theory espoused earlier this week by some like Michael McFaul, the American ambassador to Russia from 2012 to 2014.
Clinton said the cyber hacks were "not just an attack against me and my campaign".
"This is an attack against our country. We are well beyond normal political concerns here," Clinton said, before calling for a "robust" investigation by Congress into the hacks similar to the commission investigating the September 11, 2001 terrorist attacks. "This is about the integrity of our democracy and the security of our nation".
Clinton also attributed her defeat in battleground states to the 11th-hour letter sent by FBI Director James Comey to lawmakers, where he once again raised the spectre of finding more emails from her private server, months after the agency concluded its investigation and just days before the election.
Citing political analyst Nate Silver and his interpretation of available data, she said "swing state voters made their decisions in the final days, breaking against me because of the FBI letter from Director Comey".
"Nate Silver believes - I happen to believe this - that that letter most likely made the difference in the outcome," said Clinton who has remained largely out of the public eye since her Republican rival Donald Trump's victory on November 8.
Clinton's remarks came as the Obama administration has pledged to take action against Russia for the hacking attacks.