Adams was speaking to the Public Accounts Committee (PAC) along with BBC trust chairman Lord Pattern, BBC director general Lord Hall and BBC trust member Anthony Fry.
They were being grilled by a cross-party group of MPs, led by Margaret Hodge, over the £25 million paid to 150 outgoing executives between 2009 and 2012.
Adams was criticised in her role of the pay-out given to former deputy director-general Mark Byford, who received £949,000 when he left two years ago.
Adams, who is paid a salary of £320,000, said Byford had an expectation of a payment in lieu notice of 12 months because it had become "custom and practice" at the BBC.
A culture of 'cronyism'?
The session in the House of Commons follows a National Audit Office (NAO) report last month that showed large payments were made even though executives were not always entitled to the money.
The report found although most of the payments were in compliance with employment contracts, 14 cases involved people receiving money that they weren't entitled to.
One recent example that concerned politicians was the £450,000 given to previous director-general George Entwistle, who stepped down after just 54 days because of the Jimmy Savile scandal.
One MP described the benefits afforded to some top staff as "corporate fraud and cronyism".
Adams rejected this claim but did accept there was a culture "which clearly did not deliver value for money".
Adams, who was urged to consider her position by one member of the committee, said: "I have accepted responsibility for decisions made in error. We would accept the numbers in the NAO report that too often we were too generous."
She admitted a "highly litigious individual" was awarded a bigger payout than they were entitled to "in order to avoid future legal claims".
"Decisions were made with a view to saving huge amounts of money and getting senior individual managers out of the door," she added.
Shock and dismay
Pattern began by telling MPs the size of severance payments made to senior BBC managers was a matter of "shock and dismay".
Asked why he did not know some pay-offs had gone beyond what was contractually needed, Pattern appeared to suggest former director-general Mark Thompson should be called to give evidence.
"If you call a previous director general of the BBC I will be as interested as you are why we didn't know," he said.
Hall told the committee that the culture in the BBC that allowed these payouts had been "accepted but was wrong".
"We'd lost the plot. We'd got bedevilled by zeros on salaries. There was not enough grip at the centre of the organisation. Things were devolved far too low down," he said.
In April, Hall announced plans to cap severance payments that departing BBC executives and managers can receive. The limit is expected to be £150,000 or 12 months' salary, whichever is lowest.