Caroline Thomson was speaking after a damning report found the charity had a "culture of tolerating poor behaviour" and failed to report child abuse claims against some of its staff in Haiti.
The Charity Commission has examined Oxfam's handling of allegations that its aid workers used prostitutes following the 2010 earthquake in the Caribbean country.
Following an 18-month investigation, the regulator found Oxfam "repeatedly fell below standards expected, had a culture of tolerating poor behaviour and... failed to meet promises made on safeguarding, ultimately letting everyone down".
Questioned by Sky News, Ms Thomson said: "I cannot sit here and promise that these sort of incidents will never occur in the future."
She said that was because the charity works in "some of the most dangerous territories in the world - lawless areas".
She added: "We have aid workers at the moment risking their lives helping ebola sufferers in the Democratic Republic of Congo, we have people being bombed every night in Yemen.
"These are very tricky areas and it is very difficult to absolutely be sure, every time, what is happening there.
"What we need to do is to create the right culture which makes activities such as sexual abuse unthinkable or less thinkable and a culture as well where people feel safe to report it and that's crucial and that's terribly difficult in the field.
"And then a culture where once it's reported we properly investigate and we properly hold people to account and people lose their jobs over it."
Oxfam did not report allegations of child abuse by its staff in Haiti and failed to adequately investigate claims against a charity "boss" that children as young as 12 or 13 were victims of sexual misconduct, according to the 142-page report.
Its failings amounted to "mismanagement", the Charity Commission said, prompting the regulator to issue it with an official warning.
Charity Commission chief executive Helen Stephenson said: "What went wrong in Haiti did not happen in isolation.
"Our inquiry demonstrates that, over a period of years, Oxfam's internal culture tolerated poor behaviour, and at times lost sight of the values it stands for."
Ms Stephenson added that "significant further cultural and systemic change" was required at Oxfam - which has been led by new chief executive Dhananjayan Sriskandarajah since January - to address the failings and weaknesses.
The Charity Commission criticised Oxfam for not trying harder to substantiate allegations of physical abuse, made via email from a 12-year-old and a 13-year-old girl, which were "suspected" not to be genuine by the charity at the time.
The risk to victims "appeared to take second place at times" and was not taken seriously enough, and victims, whistleblowers and staff who tried to raise concerns were let down.
Oxfam aid workers were alleged to have used prostitutes in Haiti after the devastating earthquake in 2010 and in Chad in 2006.
The claims were first published a year ago and resulted in more than 7,000 people cancelling their donations, forcing Oxfam to make £16m of cuts to its aid projects worldwide.
Oxfam held its own investigation following allegations by a whistleblower in 2011, which resulted in four people being sacked and three others resigning.
The aid worker at the centre of the scandal, Roland van Hauwermeiren, had reportedly joined Oxfam after he left another British charity over similar allegations of sexual misconduct.
Mr van Hauwermeiren - Oxfam's former director in Haiti - resigned from his role with medical relief charity Merlin in Liberia in 2004 after an investigation into sex parties with local young women, according to humanitarian news website Irin.
He denied the allegations but agreed to stand down, it added.
Oxfam also faced allegations prostitutes were used by its staff in Chad in 2006, where Mr van Hauwermeiren was the charity's country chief at the time.
Following the Charity Commission's report, Oxfam apologised for its "failure to prevent sexual abuse by its former staff in Haiti".
Ms Thomson said the Commission's findings were "very uncomfortable for Oxfam GB but we accept them".
She added: "We now know that the 2011 investigation and reporting of what happened in Haiti was flawed; more should have been done to establish whether minors were involved."
The charity has tripled the amount of money it spends on safeguarding, has got 100 investigators covering every country it works in, and every member of staff has been through online safeguarding training, Ms Thomson said.
She told Sky News she was "thoroughly ashamed" of what had happened.
She continued: "'I want to say sorry. I want to apologise to the people of Haiti, to the people who were affected and the survivors of that behaviour.
"But also to our donors and supporters in Britain because we let them down.
"It was a shameful incident and it should never have been allowed to happen and should have been stopped earlier than it was."
The allegations against Oxfam were described by Prime Minister Theresa May in 2018 as "absolutely horrific" and resulted in celebrities including actress Minnie Driver and singer Tallia Storm stepping away from their involvement with the charity.