Speaking on the sidelines of The Nantucket Project conference, Diamond also said banks can't be prevented from failing-because they need to take risk to drive the economy and create jobs. But in the " Squawk Box " interview, he stressed that the "toolkit" to end the risk of taxpayer bailouts of financial institutions in the U.S. and the U.K. is available.
"The single most important thing if we're going to be able to say, 'Never again, no taxpayer money again,' is to have an effective, rigorously tested resolution and recovery plan that's accepted by the major governments around the world," he said.
"I don't think what we're trying to do is say, 'Banks can't fail,'" he added. "I think we want to be comfortable that if a bank does fail or if a bank does get into trouble it doesn't create systemic risk and it's not a burden on the taxpayers."
U.S. and U.K. banks are stronger than before the 2008 financial crisis, he said.
Diamond was ousted as chief executive of Barclays in August 2012 following the scandal surrounding the bank's manipulation of the London Interbank Offered Rate ( Libor ), which led to $442 million in fines.
"When looking back, which is important to do from time to time, that was a very difficult period for me. It was a very difficult time for Barclays. It was a difficult period for banks. It was a difficult period for the U.K.," he said. "Barclays has become a better and stronger institution. ... I'm bullish on Barclays."
"You had a situation at Barclays last summer, where the strategy was from the board to settle quickly, settle early, settle with the support of the regulators," he said.
Asked about JPMorgan and the multiple government investigations into that bank's liability for selling shoddy mortgage securities, Diamond said, "There's been criticism about maybe it's taking too long to settle."
JPMorgan boss Jamie Dimon met Thursday with U.S. Attorney General Eric Holder at Justice Department headquarters in Washington.
"If we look at the evidence and the facts, Jamie's been a strong chief executive," Diamond said. "I think JPMorgan is a stronger institution today than when we when he came. His stewardship during the financial crisis was strong."
"The theme at our conference in Nantucket is truth and the consequences of truth," Diamond added. "The truth is that banks like Barclays and JPMorgan were very steady during the worst of the financial crisis."
He added, "The ultimate arbiters of the models of banking and the management of banking are the investors. It's the shareholders. And I think that's the voice we need to listen to."