Fellow deputy chairman Rodney Baker-Bates also claimed that former Co-op Bank chairman Paul Flowers was appointed to the role due to his performance in psychometric testing.
Rev Flowers left his post last summer after the collapse of the deal to acquire Lloyds's Verde portfolio, which included Lloyds TSB Scotland, and is currently being investigated for allegedly buying illegal drugs.
Mr Davies believes regulators felt they had insufficient evidence of Co-op's weakness to stop the deal outright.
He told the Treasury Committee: "My own view is that the regulator was sufficiently uncomfortable with the deal that he would keep pushing at the capital position and, a bit like lobster in the pot, keep turning up the heat until we cracked."
Mr Davies said he was worried about aspects of the deal including a "significant error" totalling hundreds of millions of pounds in the bank's estimation of the cost of adding the Verde branches to its technology platform.
Mr Baker-Bates, who chaired Britannia building society until it merged with Co-op Bank in 2009, said: "If Verde had gone ahead you would have had a small food business attached to an enormous bank."
Mr Baker-Bates, who quit Co-op after opposing its Verde bid, added: "I thought I could not continue on something I thought was on a slope to disaster."
The two men were the only Co-op Bank directors to vote against the deal.
Mr Davies said: "The bank saw this as an acquisition that would take us from being, I would say, a division one side into the premier league."
It was later revealed that Co-op Bank had a £1.5 billion capital hole and a restructuring that has left it under the control of hedge funds.
Mr Baker-Bates, who was a candidate for chairman of Co-op Bank but lost out to former councillor Rev Flowers, said: "I was told afterwards he had done very well on the psychometric tests."
Committee chairman Andrew Tyrie said: "The two deputy chairmen of the Co-op Bank, appointed to guide a chairman with little knowledge of finance, resigned because of their opposition to Verde. Instead of ignoring their advice, alarm bells should have sounded on the main Co-op Group board."
The Verde portfolio has been rebranded as TSB with a view to floating on the stock market later this year.