Newcastle Court Magistrate Robert Stone said Wilson would be allowed to serve his detention at home due to a range of health issues he faces.
Former Archbishop Philip Wilson leaves Newcastle Local Court on July 3.
Mr Gogarty, a victim of the pedophile priest whose abuse Wilson concealed, was not the only one disappointed about the case.
He will begin this sentence staying at his sister's home on the New South Wales central coast and will be detained there until at least February 13 next year, when he will be eligible for parole.
One of the victims, Peter Creigh, expected Wilson - an assistant priest at the time - to take action after he told him Fletcher repeatedly abused him when he was 10 in 1971.
Fletcher was found guilty of child sexual abuse in 2004 and died in jail of a stroke in 2006.
He has long denied the charges and initially resisted calls to quit pending an appeal against his conviction.
Wilson, who resigned as Archbishop of Adelaide after becoming the most senior Catholic clergyman in the world to be convicted of concealing child sex abuse, showed no emotion when the decision was handed down.
However, he also found that the former archbishop had shown no "remorse or contrition" for covering up Fletcher's crimes.
However, Mr Stone said he accepted Archbishop Wilson was unlikely to reoffend.
The magistrate said Tuesday given the fact he had previously been of good character, and taking account of his age, mental and physical conditions, a home detention order was punishment enough.
Mr Stone sentenced Wilson to 12 months' jail with a six-month non-parole term for failing to report Fletcher's crimes, which he was first told about by Mr Creigh in 1976.
"Bishop O'Kelly said he was keeping Archbishop Wilson in his prayers as he formally commences this stage in his life, while also remembering the victims and survivors of abuse in the church", the archdiocese said in a statement. "Philip, will you say sorry for what you have done to me and other child sex abuse survivors?".
The Australian Catholic Bishops Conference, the country's top Catholic body that Wilson once led, had no immediate comment on his sentencing to home detention.
Despite Pope Francis accepting his resignation letter, sent on July 20, Wilson, who has been on bail since May, is "convinced of his own innocence", according to the SA church's acting boss.