He was commenting on the findings of the Commission of Investigation into clerical sex abuse in the Catholic archdiocese of Dublin.
Mr Murphy said this level of deference had no place in the garda force of 2009 and would not be tolerated "under my watch".
In response for calls to bring in outside help with the examination of the findings, Mr Murphy said his force had the experience to carry out a thorough investigation.
He had appointed a very experienced investigator, assistant commissioner John O'Mahony, to oversee a team examining how the complaints of sex abuse were handled by church and state authorities.
After he had studied a report from Mr O'Mahony, he would then consult with the Director of Public Prosecutors, who would ultimately determine if there should be criminal charges brought.
He said a plethora of complaints over behaviour in the archdiocese were already under investigation by detectives.
Asked if retired gardai could be arrested as part of the inquiries, he said the law of the land applied to all garda investigations.
He reiterated that garda investigations must never be influenced by the profession of a suspect and must concentrate on dealing sensitively with victims, applying the best investigative methods and placing a case before the courts to secure a just outcome.
The focus of Mr O'Mahony's investigation was to establish whether the failings, identified in the commission's report, amounted to criminal behaviour, he added.
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SIC: II