About 7,000 people have stopped making regular donations to Oxfam since it emerged some of its staff used prostitutes in Haiti, MPs have heard.
Oxfam boss Mark Goldring apologised to the International Development Committee for the damage done to people in Haiti and the wider efforts of aid workers.
He said 26 claims of sexual misconduct were made since the scandal broke.
Save the Children chief executive Kevin Watkins told MPs the charity had investigated 53 allegations in 2016.
Mr Goldring and two other senior Oxfam executives, faced an uncomfortable morning of questions from MPs about the sexual misconduct of the charity's workers in Haiti after the earthquake in 2010.
He also apologised for remarks made about murdering babies in cots, which he made when defending Oxfam.
In an interview with the Guardian last week, he said: "The intensity and ferocity of the attack makes you wonder, what did we do? We murdered babies in their cots?"
Mr Goldring, who joined the charity as chief executive in 2013, said he was "deeply sorry" for the comments that he had made while "under stress".
How the Oxfam scandal unfolded
The urgent session, called by the committee in response to allegations appearing earlier this month in the Times newspaper, was marked by repeated apologies.
Oxfam, which has almost 10,000 staff working in more than 90 countries, has denied a cover-up but its handling of the scandal is being investigated by the Charity Commission.
Since the story broke, Mr Goldring said 26 reports of recent and historic incidents have been made by Oxfam workers – 16 of them outside the UK.
Of the scandal, he said: "I am sorry, we are sorry, for the damage Oxfam has done both to the people of Haiti but also to wider efforts for aid and development by possibly undermining public support."
He denied there had been a cover-up, saying Oxfam had been trying to deliver a huge programme with 500 staff and his predecessors would have believed they were making the right decision at the time. "I don't defend that decision," he said.
Mr Goldring told MPs that at the time of the original investigation, Oxfam issued a press release revealing its findings of "serious misconduct" involving bullying, intimidation and breaches of the charity's code of conduct – but did not mention sexual exploitation.
"At the time, people thought that was being transparent. We know now that that was not enough," said Mr Goldring.
"I suspect there was a balance of saying 'Oxfam is delivering life-saving assistance to a million people in Haiti. We have got to keep that work going'."
He added that Oxfam had wrongly believed it was being proactive. "Not every organisation chooses to tell the public about something they got wrong," he said.
Caroline Thomson, the chair of trustees, and Winnie Byanyima, executive director of Oxfam International, both told the committee they were "ashamed" of what happened in Haiti.
Ms Byanyima said she has spent her life protecting women. "This is painful for me," she added.
Ms Thomson, who became chairwoman of Oxfam's trustees in 2017, said the charity council's task was to ensure it is "never again" at risk of being perceived to have put reputation over accountability.
Mr Goldring said there was now a safeguarding team and helpline at Oxfam and the charity was seeking more independent support.