The action was brought by Nuala Creane, whose son Sebastian was stabbed to death by Shane Clancy at their home at Cuala Grove, Bray, on August 16, 2009. Clancy took his own life on the same date.
Another of Mrs Creane's sons, Dylan, and Jennifer Hannigan, who was Sebastian's girlfriend and an ex-girlfriend of Clancy, were seriously wounded by Clancy in the attack.
Mrs Creane brought High Court proceedings because of her family's unhappiness with the manner in which an inquest into Clancy's death, which returned an open verdict, was conducted by the Coroner for East Wicklow, Cathal Louth.
She claimed that before the inquest she and her husband met the Coroner, who she says made representations about how evidence about Clancy's relationship with antidepressants and his behaviour on the night would be treated.
As a result, Mrs Creane said she and her husband decided to stay away from the inquest. However she claimed that, despite the reassurances, Mr Louth failed to conduct the inquest in a fair manner.
Earlier this year the Creanes complained about the coroner's conduct to the minister and requested a new inquest.
They also sought an order directing the minister to consider their complaint properly. Yesterday Mrs Creane's counsel, Mattias Kelly, said a reply by the minister was "no response to the complaint" and had "answered questions not asked."
The minister denied Mrs Creane's claims.
His lawyers said that the family were informed by the minister that he had "no role role in individual cases".
Yesterday in his judgment, Mr Justice John Hedigan dismissed Mrs Creane's action, as he was satisfied the minister had made his decision manifestly clear to the Creanes.
The judge, who noted the very tragic circumstances surrounding the case, said the minister had "clearly, politely but very firmly had said no".
Following the ruling, Feichin McDonagh, for the minister, said the minister was not seeking his costs of the action.
Separately Mrs Creane had also brought proceedings against the Attorney General, arising out of her refusal to order a new inquest.
That action was compromised earlier this year after the AG agreed to consider afresh the Creanes' request.
Yesterday Mr McDonagh told the court that the Attorney General had again decided not to order a new inquest.