Mr Murphy's admission came a week after the NT's corruption watchdog announced a finding of improper and unsatisfactory conduct against an unnamed public official who had mismanaged a conflict of interest in the recruitment of a senior officer.
"I found that the conduct involved negligence and incompetence … result(ing) in a substantial detriment to the public interest," Delegate for the Independent Commissioner Against Corruption Patricia Kelly SC said in a public statement.
The ICAC report revealed that in early 2024, the officer had sat on a panel that hired one of their friends.
The Northern Territory Police Association has called for Mr Murphy to resign, saying its members' trust has been destroyed and they will "not forget this betrayal".
"Our members are fed up with the lack of integrity shown and question the commissioner's ability to remain in his position," NTPA president Nathan Finn said.
On Thursday, Mr Murphy admitted that the findings related to a recruitment process he had chaired, and he accepted that he "should have dealt better with a conflict of interest, a friendship and a referee report in relation to an appointee".
"On reflection, I should have managed the friendship and the conflict of interest to a higher standard and on at least one occasion should have recused myself from the appointment process in order to ensure community confidence," he said.
Chief Minister Lia Finocchiaro said the unsatisfactory conduct was "disappointing and falls well short of the expectations the community places on the public service, especially senior executives within the public service".
On Thursday, before Mr Murphy revealed he was the subject of the ICAC finding, Ms Finocchiaro said she had been told by ICAC that she could not name the official, and she "shared the same frustrations as the community surrounding this whole situation".
But Independent MLA Justine Davis rejected Ms Finocchiaro's assertion that she could not name the official.
"ICAC is forbidden from naming anyone personally, but the chief minister is not," she said.
"If there's a senior public servant who is making decisions over things that impact on my life and my community's life, and they've been found to do something wrong, I want to know what's being done to address that, and I want to know who they are," she said.
Mr Finn said the association's executive board was unanimously calling on Mr Murphy to resign after yet another example of the police executive "failing to uphold the very standards they demand of others".
"It is a slap in the face to the hardworking men and women on the ground who put their lives on the line every day," he said.
The association has "grave concerns" over the potential complicity of other panel members in the commissioner's unacceptable conduct, he said.
"To say that the applicant was awarded the position on merit in this case is not sustainable when such a clear conflict of interest existed and was not managed," Mr Finn said.
Mr Murphy defended other executive police appointments made in the previous 12 months, saying they were "awarded to the most meritorious and best candidates".
He had accepted the two recommendations made by the ICAC regarding recruitment and conflicts of interest and was implementing them, he said.
