Five years later, Benmosche said believes that at some point there will be another financial crisis. "There's always a possibility that there will be a 'whale.' On the other hand, we've got to make sure the 'whales' don't sink the financial system."
He said he believes the Federal Reserve's stress tests on financial institutions are an important tool in preventing that from happening. "The way risk assets are calculated … there's very little chance that you'll sink the financial system. But you can cause a pretty bad bellyache for some of the big financial companies."
"If you go through most of the assets, most of the liabilities that sit in these financial institutions, I'm pretty sure we're getting our arms around it," he added.
"I always fear what I don't know," he continued, "[so] leave a little flexibility for the people who are empowered by the public to run our governments to make sure they have enough latitude to fix" any future crises.
Benmosche argued that the Dodd Frank Wall Street reform law—the government's answer to the 2008 crisis—is "basically precluding that." He added he worries about the notion that "'the policy is good enough, and smart enough; that human beings don't have to use their noodle.'"
As for who should be the next Fed chairman, Benmosche did not say whether he's backing Janet Yellen, central bank vice chair, or Larry Summers, who most recently advised President Barack Obama on economic matters.
Whoever gets the job needs to "use common sense and judgment," Benmosche explained, but added he worries about the pressure on Summers for the role he played as Treasury secretary in the 1990's deregulation of the financial industry.
—By CNBC's Matthew J. Belvedere; Follow him on Twitter