David Thorburn, chief executive of Clydesdale Bank, said with the "benefit of hindsight" a number of customers got something which they did not fully understand.
But one customer said they felt the apology was a smokescreen.
While Mr Thorburn acknowledged the bank put an emphasis on the sale of products it felt were unique in the market, customers should not have felt pressured into taking on that type of borrowing.
He said: "Sometimes staff overstepped the mark and when we find evidence of that we will fix it."
Jim McGrory, a St Andrews hotelier whose complaint against Clydesdale has been upheld by the financial ombudsman but is waiting on redress, said: "None of the customers want to work with [Clydesdale] anymore. They want away. The main problem most of us have is our credit records will be damaged so when we go to refinance the chances of us rebanking [with someone else] are very slim.
"I don't think they will ever recover the trust of customers."
Giulio Girasoli, who runs the Little Flowers Nursery at Renfrew, has left Clydesdale after waiting for a loan to expire as he could not afford the break fee but complained to the ombudsman. He felt the regret expressed by the bank was not genuine and said: "It is a smokescreen for the TV. They have done nothing to recompense myself."
Mr Thorburn was giving evidence in front of the Treasury Select Committee yesterday as part of its inquiry into lending to small and medium enterprises.
The Glasgow-based financier said Clydesdale, which is owned by National Australia Bank (NAB) had regret around a number of the most complex loans, which were meant to protect customers if interest rates went up, it had sold and it was "very sorry".
Allegations of mis-selling were first reported in The Herald in July 2012. According to Mr Thorburn's evidence, the proportion of cases where customers were sold products which were unsuitable is very small. He said: "What we have found as we have gone through several thousand files is there are some exceptions but that kind of behaviour is not widespread."
The NAB Customer Support Group, made up of SMEs in dispute with Clydesdale, said: "The banks now realise that the mis-selling of fixed-rate business loans embedding derivatives is no longer being ignored by Parliament and that there will soon be government intervention that will prevent further damage to the economy arising from this activity."
Mr Thorburn suggested the plunge in interest rates to 0.5 per cent and the non-movement from that level had led to higher costs.He said: "We didn't see that interest rate scenario happening as it had never happened in history."
When asked whether it had been a mistake to sell the most complex loans to SME customers Mr Thorburn said: "Yes, definitely."
Mr Thorburn was joined at the committee by Debbie Crosbie, the bank's executive director for customer trust and confidence.
She confirmed Clydesdale is looking into around 550 cases which have not been included in a separate mis-selling review by the Financial Conduct Authority.
The bank expects to pay redress in 60 per cent of the cases.