In a message sent to the bank's 75,000 employees, the banker said that anyone can make mistakes while insisting that staff had to maintain the highest professional standards.
“I don't expect anyone to get everything right all the time. The important point being how we learn from those mistakes and the decisions and actions we take afterward,” he wrote.
Horta-Osorio, married with three children, has remained silent amid claims he had a relationship with Wendy Piatt, a former aide to Tony Blair. The couple were pictured together during a business trip in Singapore in June.
The chief executive allegedly paid a hotel bill of nearly £4,000 during his stay with Piatt.
Lloyds Bank, bailed out by taxpayers for £20 billion during the financial crisis in 2009, said it had examined Horta-Osorio’s expenses in Singapore and cleared him of any wrongdoing.
"I deeply regret being the cause of so much adverse publicity and the damage that has been done to the group's reputation. It has detracted from the great work which you do for our customers on a daily basis and from the major accomplishments of the past five years," Horata-Osorio wrote.
In his message, which you can read in full here, Horta-Osorio added that the bank was prepared to cope with the extended period of low interest rates and a weakening economy,
“As UK focused bank we are not immune to the factors likely to shape the UK economic outlook, but I believe we will be well positioned to meet them,” he said.
Last month, Lloyds announced it would be cutting 3,000 jobs and closing 200 branches despite doubling its pre-tax profits.
A statement from the group announced it had enjoyed a £2.5 billion profit in the six months to the end of June, compared to £1.2 billion in the previous half year.
The decision was part of plan to pare about 9,000 roles by 2017, the London-based bank said in a statement at the time. The losses were in divisions such as consumer operations, risk management and finance.
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