Federal Reserve Chairman Ben Bernanke told a panel investigating the financial crisis that regulators must be ready to shutter the largest institutions if they threaten to bring down the financial system.

“If the crisis has a single lesson, it is that the too-big-to-fail problem must be solved,” Bernanke said Thursday while testifying before the Financial Crisis Inquiry Commission.

Bernanke also said it was impossible for the Fed to rescue Lehman Brothers from bankruptcy in 2008 because the Wall Street firm lacked sufficient collateral to secure a loan. Lehman’s former chief executive told the panel a day earlier that the firm could have been saved, but regulators refused to provide help.

The Fed chief presented his analysis of the crisis and views on potential systemwide risks as the panel approaches the end of its yearlong investigation into the Wall Street meltdown.

The financial overhaul law enacted this summer gives regulators the authority to shut down firms when their collapse poses a broader threat to the system. The process resembles the one used by the Federal Deposit Insurance Corp. to close failing banks.

FDIC Chairman Sheila Bair told the panel “the stakes are high” for regulators to effectively exercise their new powers.

If not, “we will have forfeited this historic chance to put our financial system on a sounder and safer path in the future,” Bair said. ”The tools are there. The regulators have to use them,” she testified.

Panel Chairman Phil Angelides said the new law will be an enormous test of will of the regulators.

Bair and Bernanke said tougher rules and market pressures will lead huge firms to voluntarily shrink themselves. Executives can no longer count on the government to bail them out if they veer toward failure, they said.

Bernanke said that bailing out these institutions is not a healthy solution and great improvement will come from the new law.

“Too-big-to-fail financial institutions were both a source … of the crisis and among the primary impediments to policymakers’ efforts to contain it,” Bernanke said.

“We should not imagine … that it is possible to prevent all crises,” he said. “To achieve both sustained growth and stability, we need to provide a framework which promotes the appropriate mix of prudence, risk-taking and innovation in our financial system.”

Bernanke led the economy through the financial crisis and the worst recession since the 1930s. The Federal Reserve took extraordinary measures to inject hundreds of billions into the battered financial system.

Last week he said the central bank is prepared to make a major new investment in government debt or mortgage securities if the economy worsened significantly.

Members of the congressionally appointed panel have questioned the government’s decision to let Lehman fall while injecting billions of dollars into other big financial institutions during the crisis.

Former Lehman CEO Richard S. Fuld Jr. testified Wednesday that the firm could have been rescued. But the regulators refused to help — even though they later bailed out other big banks.

Bernanke disagreed. He said bailing out Lehman would have saddled the taxpayers with billions of dollars in losses.

“It was with great reluctance and sadness that I conceded there was no other option” than allowing Lehman to fail, he said.

Asked how the Lehman case differed from that of American International Group Inc., which received $182 billion in taxpayer aid, Bernanke said there was a fundamental difference.

AIG, as the biggest insurance company in the U.S., had valuable assets which could back up the Fed’s emergency loan, he said.

“The Federal Reserve will absolutely be paid back by AIG,” Bernanke said.