"We saw in 2007 to 2008 how bad consumer practices could actually accumulate and contribute to a financial crisis," he said. "We need to protect consumers and we also need to protect the financial system, and we shouldn't be rolling back Wall Street reform."
Lew said the Wells Fargo sales scandal isn't as bad as what took place before the financial crisis, but is "bad enough that it just takes away people's confidence and trust in their own banking relationship."
The bank in September agreed to a $185 million settlement for violations by its community banking division for opening about 2 million accounts without customer authorization starting in 2011. The settlement included $100 million with the CFPB, the largest penalty the agency has ever imposed.
In September, Lew said at the 2016 Delivering Alpha conference presented by CNBC and Institutional Investor that the Wells Fargo case should be a "wake-up call."
"This ought to be a moment where people stop and remember how dangerous the system is when you don't have the proper protections in place," Lew said.
The CFPB was created as part of the Dodd-Frank financial reform act following the financial crisis. Republican presidential candidate Donald Trump has pledged to repeal those changes.
But lawmakers like Rep. Jeb Hensarling, chairman of the House Financial Services Committee, demanded to know why it took so long for regulators to take action against Wells Fargo.
"Why was the story broken by an LA Times reporter years and years ago and only now … have our regulators seemingly caught it?" the Texas Republican said on CNBC's "Power Lunch." "I don't know if they need a pat on the back or a swift kick in the backside."
Earlier this month, a U.S. appeals court ruled that the structure of the CFPB is unconstitutional because the financial watchdog's director wields too much power. Hensarling has recommended reforming the CFPB so that it is run by a five-member bipartisan commission instead of a single director.