MPs repeated calls for Jonathan Ross's head to roll over the Andrew Sachs prank calls row.
But Sachs's granddaughter Georgina Baillie, 23, said she was happy with the findings.
The burlesque dancer at the centre of the controversy over Russell Brand's Radio 2 show issued a statement through publicist Max Clifford.
In it, she said: "I am pleased that the BBC took the time to do such a thorough investigation.
"I am happy with the findings and the new procedures which have been put into place to ensure that this type of incident does not happen again.
"It is now time to draw a line under the matter and move on."
Speaking at their family home in Kilburn, north west London, Sachs's wife Melody said: "My husband is the most wonderful person you could ever meet. They just picked on the wrong man."
Mrs Sachs said the family was "tired" of the so-called "Sachsgate" affair, but said they had "no bitterness at all" towards the BBC presenters.
"Andrew has got nothing to say," she said.
"I don't suppose he wants to do anything more about it. We are so tired of all this stuff. Whatever they do, they do, but we are so tired of it all.
"We are the happiest people in the world. Andy is fine and that's all that matters."
Shadow culture secretary Jeremy Hunt said the decision ignored the "fundamental issue" of putting quality programming ahead of ratings.
"The BBC Trust has sadly missed the point," he said.
"This is not simply about an editorial guideline that wasn't followed, but the BBC failing to recognise that the stars it employs should not behave in a way that legitimises behaviour that is totally offensive to the vast majority of licence fee-payers.
"A gentle slap on the wrist for the management won't address the fundamental issue: the BBC should be chasing quality and not ratings."
Labour MP Alan Simpson, who tabled a Commons motion calling for Ross and Brand to be sacked, criticised Sir Michael for not applying real-world principles to the BBC.
He said: "In any other organisation the chief executive and the chairman would have sacked the person on the spot and I think it is a measure of the extent to which either the BBC, or the media in general, feel that they are in a different world that does not hold itself to account in a way that every other institution in society would do."
Liberal Democrat Phil Willis, who also called for Ross and Brand to be sacked, said taxpayers deserved better standards for their money.
"I am disappointed that this is the result and I think that once again the BBC have demonstrated that it is one law for its highly-paid stars and one law for everyone else," he said.
"When we are forking out millions of pounds of taxpayers' money on presenters, the least we can expect is a level of propriety commensurate with what the public considers decent.
"That didn't happen in this case and I think Mr Ross should have been sacked."
Conservative MP Nigel Evans said: "I am disappointed that the Trust has failed to take this opportunity to examine both the Trust's and the director-general's slow reaction to this entire affair.
"It is now left to Ofcom to independently investigate this particular set of events and I hope that it will come up with a firmer and harder-hitting conclusion than that of the Trust."
But Liberal Democrat shadow culture, media and sport secretary, Don Foster, said: "The necessary steps being taken by the BBC Trust to strengthen editorial guidelines in the wake of this damaging incident are welcome.
"Sacking Jonathan Ross would not prevent this from happening in the future.
"Editorial guidelines are there to prevent entertainers from over-stepping the mark and the BBC must now ensure that high-risk shows are properly scrutinised in the future."