Speaking to the Financial Crisis Inquiry Commission (FCIC), Mr Bernanke said the firm was in such a poor financial position that an emergency injection of state funding would have been unjustifiable.
Dick Fuld, the former boss of Lehman Brothers, has previously claimed that the failure of the financial institution was down to a refusal of government support combined with unjustified panic on the markets.
But Mr Bernanke rejected this version of events in his testimony, stating that he wished he had done more in the past to rectify "the mistaken impression that in fact we could have done something", reports the Guardian.
When Lehman suffered a bank run in the lead-up to its collapse in September 2008, the Fed chairman said the regulator was right not to act, as the firm's lack of capital meant it could not have been saved.
This would have then left taxpayers with "tens of billions of dollars of losses", said Mr Bernanke.
"The only way we could have saved Lehman would have been by breaking the law and I'm not sure I'm willing to accept those consequences for the Federal Reserve and for our system of laws," he added.
Mr Bernanke stated that he wished it had been possible to rescue the firm from bankruptcy, but it was "beyond the ingenuity and capacity" of the Fed to manage it.
Earlier this year, former British chancellor Alistair Darling stated that he was shocked when the US government allowed Lehman Brothers to go to the wall, reported Bloomberg.
He said he had blocked a potential Barclays takeover of Lehman Brothers because he did not want a British firm underwriting a whole American bank.
By Gary Cooper