Ms Therese Willoughby, the mother of Brian Willoughby, said the Court of Criminal Appeal had delivered "an injustice" against her son by failing to hear new medical evidence in the case.
Ms Willoughby, who had fought in vain for the State to provide treatment for her son's violent behaviour prior to the murder of Brian Mulvaney in March 2000, said yesterday: "We are totally drained. I can't really describe our feelings.
"I know there is a lovely young man dead but our son was not in his right mind when this happened. I can't understand the injustice of it."
Ms Willoughby had previously indicated that she might sue the State for its failure to provide services for her son, who suffered from attention deficit disorder and serious behavioural problems.
However, following yesterday's ruling, she said: "We cannot do anything any more. We are finished. There is nobody who can do anything for us now."
She added that "scurrilous headlines" in the media during the appeal had brought more pain on her family. "We certainly are at the front of it all, all of the time. We would rather be the Mulvaneys."
Mr John Lonergan, governor of Mountjoy Prison, where Willoughby is serving a life sentence, has described as "a scandal and a disgrace" the fact that families such as the Willoughbys had been unable to get help from the State to deal with children with brain and behaviour disorders.
Speaking after Willoughby's conviction last April, Mr Lonergan said: "Brian Willoughby is a madman. He needed help as a young boy and, despite his parents' efforts, he did not get it, because the help does not exist in this country."
