Father Oliver Kemp, from Stone, served at Catholic churches across the region during his career including in at St Joseph's Church, in Darlaston.
He was fatally assaulted at hospital site off Weston Road, Stafford, on February 17 last year and died from his injuries six days later.
On Thursday, Joseph David Phillips pleaded guilty to the manslaughter of Father Kemp by reason of diminished responsibility at Stafford Crown Court.
Paying tribute, the Archdiocese of Birmingham said: "We acknowledge today's plea and keep in our prayers the late Father Oliver Kemp and all those who mourn him.
"As a diocesan family we remain deeply saddened by Father Kemp’s passing in such tragic circumstances.
"He was a retired priest of the Archdiocese of Birmingham and served at several parishes across the archdiocese from his ordination in 1966 until his retirement in 2004.
"We commend Father Kemp to the Lord, that he may he rest in peace, and we pray for all those affected by his death."
Phillips will be sentenced on September 6 after evaluations by psychiatrists.