The Prime Minister's comments come a day after the independent report's publication, which reveals two of four individuals involved in the mistakes have been suspended.
The report by the HM Inspectorate of Probation, Dame Glenys Stacey, found serious failings by the probation service prior to the murder of Lisa Skidmore.
Her killer Leroy Campbell was released from prison without suitable supervision, said the report, which concluded her death was 'entirely avoidable'.
Campbell had only been free from prison for four months when he raped and strangled the 37-year-old district nurse in her home.
He had earlier told a probation officer he was thinking of raping again, but no action was taken to recall the the 57-year-old killer to prison.
At Prime Minister's Questions today , Wolverhampton South East MP Pat McFadden put the findings of the report to Mrs May.
"Lisa was let down in the most appalling way, by a service which is there to monitor offenders and to protect the public. And in this case, failed to do so with the most devastating consequences."
Mrs May responded by saying she hoped the review would go some way towards making sure this never happens again.
She said: "I understand that some action has already been taken, two members of the probation service have been suspended.
"Whilst nothing can done to bring back Lisa, or to minimise the impact that this has had on her family, Dame Glenys Stacey has been asked to conduct an independent review to look at what can be done to prevent such tragedies from happening again to make sure this never happens to anybody else."
The investigation into the case was ordered by Justice Minister Rory Stewart, who has met the family of Mrs Skidmore on several occasions to discuss their concerns.
It highlighted a lack of lack of action taken by the probation service when, a month before Campbell carried out the murder, he told an officer he was thinking of raping again.
The report said the service had failed to protect the public with 'significant failures in practice, recording and management oversight'.
The probation officer who Campbell made the disclosure to was covering for a colleague who was on holiday and was supervised by an officer who was not familiar with the case.
The supervisor failed to record the disclosure adequately, the report said.
But neither will face disciplinary action.
However, another supervising officer who failed to make a decision to return Campbell or recall him to prison is to face disciplinary action and has been suspended.
A probation officer responsible for preparing Campbell's release from prison four months prior the murder will also face disciplinary action and is suspended.
That officer 'showed a lack of diligence' according to the report, which said appropriate risk management and supervision were not applied to Campbell.
The report said: "Campbell was a man who had demonstrated that he was capable of serious offending and by any standards should have been managed robustly.
"Failing to put in place arrangements for police, probation and other agencies actively to manage him jointly through multi-agency public protection arrangements was a significant gap in the preparation for his release.
"Not responding and appropriately signs of escalating risk was a major failure."
Executive director of National Probation Service, Sonia Crozier, said she was 'deeply ashamed' over the failings.
Miss Skidmore was killed in November in 2016 by Campbell, who is now serving a life sentence for murder.
Miss Skidmore's sister Alison Parker responded to Mrs May's assurance.
She said: "People say lessons are to be learned but unless something is put in stone and people are held account for their action, these things will keep happening.
"I don't believe it."
A pre-inquest review into her death will decide on Thursday if the parole board's decision to release Campbell from prison before the murder should be questioned.