The corporation broadcast its apology on Radio 2 on Saturday morning and Saturday evening.
However, Sachs telephoned the BBC after hearing the first broadcast and asked for the second apology to be changed, pointing out his his wife and daughter were deeply hurt by the affair.
In the apology the BBC also said sorry to licence fee payers and said the telephone calls to the actor's answering machine should never have been made.
Sachs said he asked for the wording of the apology to be changed because his wife was "more emotionally affected" than him by the controversy.
Sachs said: "I was surprised that I was not contacted before the apology was broadcast. They could have saved themselves a lot of trouble and it annoyed me a bit that I was forced to call and tell them to change it."
The apology came hot on the heels of yet another resignation as the fall-out from the scandal continues.
On Friday, David Barber, Radio 2's head of specialist music and compliance, whose job it is to ensure that all content broadcast complied with BBC guidelines, resigned.
His departure follows that of Lesley Douglas, Radio 2's controller, and Brand himself.
In an interview with The Observer Music Monthly magazine published yesterday, Brand said the recording of the obscene messages left on the answering machine of Sachs had been toned down before it aired.
Brand said: "We took out the more personal stuff."
Brand also said that he and his guest, Jonathan Ross, who has since been suspended for three months by the BBC, were reassured by their producer that Sachs had approved the contents of the pre-recorded radio show.
He revealed: "The grey area is that our brilliant young producer, Nic Philps, called Andrew Sachs afterwards and said, 'Is it OK? Can we use it? Do you mind?' And he said, 'Oh yeah, but can you tone it down a bit?' So we did."
The saga is set to continue with the results of the BBC and Ofcom's investigations due in the near future, while Channel 4 is following Five in airing a documentary on the events this Wednesday.
Brand's Hollywood career continues on course -- he will star alongside Adam Sandler in the forthcoming Christmas movie 'Bedtime Stories' and has recently been cast alongside Johnny Depp in the next 'Pirates of the Caribbean' film in the role of his brother.
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