Chief Constable Gareth Morgan reopened the investigation into the high-profile case last year, pledging to try to achieve justice for the victim's family, but announced in October a suspect could not be charged because of previous failings.
The outcome delivered a devastating blow for the family of promising footballer Mr Nunes, who was gunned down in Pattingham in an execution-style killing in 2002.
The force spent 18 months working on a fresh inquiry only to be told by the Crown Prosecution Service a suspect identified could not be prosecuted due to past blunders.
The original case infamously collapsed when serious police errors came to light, leading to the convictions of five men being quashed.
Now, following a Freedom of Information request by the Star, it can be revealed the new investigation cost £45,991 only to come to nothing. A team of seven detectives worked on the case, led by senior investigating officer Dan Ison.
Detectives not involved with the previous scandal-hit probe pored over thousands of documents and re-tested evidence using new techniques as part of the new investigation.
But despite all the staff hours and costs involved, the CPS ruled a case being built against a suspect could go no further because of the history, dashing the hopes of the Nunes family.
The Taxpayers' Alliance said police needed to ensure they were not wasting money.
Harry Fone, from the alliance, said: "Every effort must be made to avoid wasting taxpayers' money.
"There's no doubt the police face a very difficult task in upholding the law but the force must remember that there is a limited amount of public funds.
"Police chiefs must ensure that they get maximum value for every pound spent."
The CPS said it would have been an "abuse of the legal process" to pursue the suspect. The chief constable opted against handing the investigation over to another force last year.
Following the failure of the new investigation, Mr Morgan insisted he stood by his decision to try again to solve the killing of Mr Nunes, of Whitmore Reans, Wolverhampton.
He said: "The decision I made to reinvestigate the original inquiry was a significant one for Kevin’s family, the wider community and the force, but absolutely the right one to make.
"The original investigation was undertaken many years ago and since then things have changed significantly with robust governance and scrutiny guiding how the force operates under a new overarching legislature."