“The dirt has been swept under the carpet without any serious attempt to lift the lid on what really happened to Pat and so many others,” said Geraldine Finucane.
Ms Finucane said she accepted British prime minister David Cameron’s apology, but suggested he had little choice but to offer one.
“He is a human being. He probably does think it is an atrocious act. But unfortunately he is quite removed from Northern Ireland or what went on in the late ’80s.
“So maybe it isn’t very hard for him to apologise.
“I will give him the benefit of the doubt and accept the apology, but it doesn’t go far enough because I don’t really know what he is apologising for.”
The report “doesn’t tell me much more” than previous inquiries, said Ms Finucane.
Her son, Michael, said that while there was new material in the report regarding the extent of the threats, “it doesn’t really take you much further in terms of the culture”.
Previous reports had made clear that it was the “overwhelming priority” of agencies to protect intelligence sources even if there was a “human cost”, he said.
“David Cameron referred repeatedly in the House to what went wrong here,” he added. But “nothing went wrong here”.
“This is exactly what it was designed to do: To improve and focus the targeting abilities of loyalist paramilitaries over many years,” said Michael Finucane.
“A thorn in the side of the authorities could be removed, killed, in circumstances where the state could deny any responsibility.”
There were probably “hundreds of others” killed in similar circumstances, he added.
He said he believed there would be a public inquiry if Labour won the next UK general election, as he expected opposition leader Ed Miliband to “keep his word” on the need for one.
Ms Finucane said Taoiseach Enda Kenny had always been supportive of the family’s fight and said she would not be surprised if the Government upped the ante now.
“I expect the Irish Government to continue their support for me. I know that they have been very angry in the fact that the British government broke an agreement between the two countries unilaterally and they don’t think that that is the correct way to behave.
“So they are upset politically because that has happened and they are upset because it was such an atrocious act.
“Enda Kenny has always been very supportive. In light of this, I can’t say what the Irish Government are going to do because I haven’t spoken to them today but I wouldn’t be surprised if they would up the ante slightly.”
“Why is there this great fear by the British establishment to go examining the case of Pat Finucane in public?” asked Michael Finucane. “It’s because they have stuff to hide. It’s because they don’t want people being questioned in public.”
He said Britain did not want people like former home office minister Douglas Hogg being asked “probing questions”.
“Douglas Hogg went into the House of Commons and made a statement,” said Michael Finucane. “Now, that has been benignly characterised as a compromise of a minister where he was misled.
“Did he not understand what he was saying when he said solicitors were unduly sympathetic to the IRA? Preposterous.
“He’s a barrister himself. He knew exactly what he was doing and yet that issue is not really touched on in the De Silva report.”
He said it was “glossed over as a minister being misled”.
“The benefit of the doubt is always given to the person who is still around, who is still alive, who could still be a witness in an inquiry and that is where we have a fundamental problem with this report,” said Michael Finucane.