Two Greater Manchester Police detectives who investigated Dr Harold Shipman were unfit to handle the case, the inquiry found.
"If the police and the coroner had moved with reasonable expedition, the lives of Shipman's last three victims would probably have been saved," said Dame Janet Smith, the judge heading the inquiry.
The initial police inquiry was triggered when another doctor raised concerns Shipman might have been killing his patients.
Two officers were appointed to investigate, but "found no cause for concern" after a short enquiry.
Shipman killed at least 215 of his patients.
Lied about mistakes
Police made mistakes
According to Dame Janet, the senior officer, Chief Superintendent David Sykes did not give effective leadership, and the junior officer, Detective Inspector David Smith, was "out of his depth" and lied to cover up his mistakes.
Her findings were welcomed by victims' relatives who praised the inquiry and said it might prevent such murders happening again.
"The police made terrible misjudgments and today it's been brought into the public arena," Barry Swann, whose mother Bessie was killed by Shipman in 1997, told the BBC.
"It could happen again, but as long as these recommendations are taken on board it will go a long way to stop it."
Mr Swann added that he would await Dame Janet's final report before deciding whether to take any action against police.
Meanwhile, Greater Manchester Police unreservedly apologised to the families of the victims and said it had taken on board Dame Janet's recommendations.
Assistant Chief Constable Dave Whatton said: "The basic problem was that the wrong people were in charge... this sort of thing will not happen again." .
Shipman, 57, was jailed for life in January 2000 for murdering 15 of his patients.
The deaths of hundreds more were investigated at the public inquiry last year which found he had killed at least 215 people and probably as many as 260.