They said crucial documentation had been lost.
It follows a 20-year campaign for justice by an alleged victim of Fr James Robinson.
The man, who now lives in Scotland, said West Midlands Police failed to investigate the abuse properly when it happened, and should have extradited the former priest to face charges following his move to California.
A spokeswoman for West Midlands Police said: "We can confirm that the man has now received our findings.
"His complaint that West Midlands Police failed to investigate the Catholic Church has been substantiated.
"Although there was evidence of an investigation, a lack of substantiated documentation as a result of the historic nature of the case meant that we were unable to assess the thoroughness of any investigation."
Robinson was accused of repeatedly abusing young boys in the 1970s and 80s.
He was moved by the church to a parish in California as the abuse accusations raged in 1985, and was defrocked eight years later.
He has denied any wrongdoing, and says he has no intention of returning to Britain.
Despite the former priest being tracked down and confronted by one of his alleged victims in 2003, West Midlands Police said they were prevented from extraditing him by California state law.
A spokeswoman said: "At the time of the allegations made by the man against Father Robinson, a treaty was not in place to enable extradition from California. "
During 2006 a new treaty was ratified which means that extradition is possible. Any request for extradition is the subject of judicial procedures
West Midlands Police will review the original investigation and consider the appropriate course of action."
The alleged victim, now married and in his 40s, maintains it is possible to arrest Robinson, and has contacted California's Governor Arnold Schwarzenegger.
Robinson is alleged to have systematically abused boys while training at Oscott College, Sutton Coldfield; as a parish priest at St Elizabeth's, in Foleshill, Coventry; at Holy Family Church, in Small Heath, Birmingham; at Our Lady of Lourdes, Cradley Heath, near Halesowen; and at Father Hudson's children's home, Coleshill.
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