If bankers want to improve their reputations, they need to get better at admitting how bad those reputations are.

Despite all the evidence, some bankers are still in denial over how much their industry is disliked and mistrusted these days. That became apparent again Tuesday, during a panel discussion with high-profile industry members and critics.

"The first step in solving any problem is to admit you have a problem," Raj Date, the former deputy director of the Consumer Financial Protection Bureau, said during the discussion at New York's Harvard Club.

Date said that when he would meet with groups of bankers in the early days of the CFPB and the discussion would turn to reputation and customer relationships, the executives invariably would argue that their customers loved their banks — even at the height of Occupy Wall Street.

"Okay, dude, there are people literally sleeping in tents just to point out how much they don't like you," Date recalled thinking.

The evidence is more than anecdotal: banking is the least trusted industry, according to the Aspen Institute's Initiative on Financial Security, which hosted the panel discussion on Tuesday. The biggest banks appear to have the most work to do to repair their customer reputations: Aspen and its research partner, BAV Consulting, found that Bank of America (BAC) and Citigroup (NYSE:C) are among the least-trusted bank brands, while USAA is the most-trusted in the industry.

A Citi spokesman said the bank "is a fundamentally different company since the crisis and has returned to the basics of consumer and institutional banking." A B of A spokesman declined to comment.

Also Tuesday, Date said he was starting his own bank advisory firm. He was joined on the panel by former New York Gov. Eliot Spitzer, a veteran industry critic, and by former UBS Americas Chairman Robert Wolf, who took the role of industry defender at the event.

"Things are changing. … We should talk about how we move forward, not backward," said Wolf, a prominent fundraiser for President Barack Obama who now runs his own consulting firm.

"We understood that change needs to take place and we're changing," he said, referring to new regulations, including the Dodd-Frank financial reform law, that have been created since the financial crisis.

During the weekend of Lehman Brothers' bankruptcy, when Wolf was one of several senior bankers in the room at the Federal Reserve Bank of New York, "it was clear then that we needed regulation," he added. "We did not have the tools that day."

Spitzer, meanwhile, argued that regulation should not be necessary to improve trust in the banking industry. "Regulation's fine, but at the end of the day it cannot embed good judgment," he said. "Good judgment cannot be regulated."