Mark Thompson admitted there had been "errors of judgement"
BBC bosses have faced fierce questioning from MPs over the crude phone calls made by Russell Brand and Jonathan Ross to actor Andrew Sachs.
BBC Trust chairman Sir Michael Lyons denied the corporation had been slow in its response to the incident, but admitted lessons could be learned.
The BBC's director general, Mark Thompson, admitted "a very serious editorial lapse" had occurred.
The pair were speaking at a Culture, Media and Sport Committee hearing.
Sir Michael and Mr Thompson defended the corporation's actions in the aftermath of the scandal.
Mr Thompson revealed that he was unaware of the furore until the evening of Monday, 27 October as he was out of the country, and out of telephone contact, when details of the incident were published in a Sunday newspaper.
"I was told there had been a serious editorial breach on Radio 2 and that the BBC had issued a comprehensive unreserved apology that morning and that an inquiry had already started," he said.
Conservative MP Nigel Evans criticised the BBC's "lamentable slowness" in handling the crisis, but Sir Michael replied: "There was no lack of speed."
"I refute and reject any allegations there were more actions the trust should have taken. The trust is doing its job of holding the executive to account.
"I don't think we could've got an apology out any earlier," he added.
"Could that apology have been worded differently? It was clear that it was both an apology to Andrew Sachs and that [the broadcast's] underlying material was unacceptable."
Ross was suspended over the incident and Brand resigned.
However Sir Michael admitted that the BBC could have addressed Mr Sachs' granddaughter, Georgina Baillie, who was the subject of the crude phone calls, in its initial apology.
He added there was a case that the BBC's head of audio, Tim Davie, should have been "on the airwaves" to make a public statement a little earlier.
Davie faced the press on Tuesday, 28 October, two days after the incident on Brand's Radio 2 show came to light - but 10 days after the initial broadcast.
MPs also criticised Sir Michael and Mr Thompson for failing to fire Ross and Brand for "gross misconduct".
"The primary failing is not the antics of performers, it's the fact it was allowed to go out," Sir Michael replied.
"Until we have finished our investigations, I would be careful about terms like gross misconduct which have contractual implication," he added.
"The BBC looks at the evidence before making its decisions."
He added one of the things the trust was exploring was "whether it is right to leave a young producer implanted in a company that is owned by one of the performers", a reference to the BBC producer who was drafted in to work for Brand's production company while the star's regular producer was away.
Mr Thompson added that the corporation would be looking at whether additional safeguards were needed to ensure compliance procedures were being fulfilled in programmes made by independent production companies where the artist has an economic involvement.
Mr Thompson said the BBC had improved standards.
He added that the BBC had improved its standards over the past five years.
"We've seen progressive widespread, tightening and improving - that's not to say that we shouldn't learn lessons from individual serious lapses," he added.
When discussing Jonathan Ross, Sir Michael said he felt that Radio 2 had been premature in announcing the presenter would be returning to the station in January before the trust had completed its investigations into his role in the incident.
Sir Michael told MPs the trust had not finished its inquiry and that all decisions would follow from that, with nothing being ruled in or out.
He did, however, defend Ross's £6 million-a-year contract, saying it reflected the market rate and that some members of the public had told him the presenter was the reason they tuned in to the BBC.
Following the hearing at the House of Commons, the BBC Trust issued a statement in response to media speculation about the possibility of further action against Ross.
The Trust said it ratified BBC management's proposal to suspend the presenter for 3 months without pay.
It added: "The Trust will not pre-empt its own inquiry, but based on the oral updates it has received since 30 October, it does not expect the director general's final report to provide new information of substance relating to Jonathan Ross's role which would lead it to change its view on his part in this incident."
Mr Thompson is due to report back to the trust later this week on BBC management's findings over the furore. The trust will announce the results of their investigation on Friday, 21 November.
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