In proceedings initiated two years ago, the group complained about the failure of the Commission to report on one of its terms of reference.
Justice For the Forgotten claimed the failure was in breach of the European Convention on Human Rights.
However, Ms Justice Mary Laffoy ruled that complaints which related to events 29 years before the European Convention on Human Rights Act came into force in 2003 were 'not justiciable' in Irish law.
The group had also challenged the State's refusal to allow access to the archives of the Commission.
However, Ms Justice Laffoy said the Taoiseach was bound by the prohibition on disclosure until 30 years after the dissolution of the Commission. Therefore the plaintiffs did not have a legally enforceable right to access the archive of the Commission.
The term of reference not reported on by the Commission involved a lead in the garda investigation concerning a man who had stayed in the Four Courts Hotel around the time of the bombing and his links to the UVF.
When the Commission reported to then Taoiseach Bertie Ahern in 2007 it stated that it could not report on this matter and that an explanation had been given to the Taoiseach.
Lawyers for the group had argued that the Taoiseach was not entitled to receive such an explanation and not disclose it publicly.
After the judgment, a spokesperson for the group said they were disappointed but needed time to read the full judgment before commenting further.
