The ex-SNP minister said managers need to be held to the same standards as medics.
Yesterday, Lucy Letby was sentenced to life in prison for seven counts of murder and six counts of attempted murder.
Concerns about the killer were raised with bosses at the hospital where she worked two years before police were called in.
Whistleblowers have said babies could have survived had executives acted sooner.
READ MORE: Lucy Letby given whole life sentence for murder of babies
The Countess of Chester Hospital’s neonatal unit head consultant, Dr Stephen Brearey, first raised Letby’s association with an increase in baby collapses in June 2015.
He told the Guardian that deaths could arguably have been avoided from as early as February 2016 had managers at the hospital “responded appropriately.”
Around seven senior clinicians eventually raised concerns about Letby.
However, police were only contacted in 2017.
Dr Brearey and another consultant, Dr Ravi Jayaram were even ordered to enter a mediation process with the nurse.
Both consultants have said executives at the hospital were reluctant to involve the police for fear of damaging the trust’s reputation.
Over the weekend, the British Medical Association (BMA), the professional body for doctors repeated their call for tighter regulation of NHS managers.
In a statement, they said: “ It is vital that any inquiry looks carefully at how concerns of the most senior doctors were handled and able to be dismissed, which perpetuated this horrific and catastrophic series of events.
“The BMA has been clear that the NHS and the whole healthcare system must have an open culture where doctors are listened to and can be confident in speaking out.
“We have long called for non-clinical managers in the NHS and other health service providers to be regulated, in line with the manner in which clinical staff are by professional bodies.
“Our thoughts go out to the families and staff involved in this heart-breaking case. We must now leave no stone unturned to make sure this can never happen again.”
READ MORE: Jeane Freeman backs calls for NHS managers to be regulated
Mr Neil told The Herald: “If it is true that the medical consultants in the Lucy Letby case were threatened by their managers with losing their jobs if they took their concerns further, then these managers should no longer be allowed to hold senior positions in the NHS.
“I know from my own experience that the quality of managers is variable.
“We need to return to a policy whereby more medics are encouraged to become qualified managers.
“The changes made by Ted Heath’s government which made managers so all-powerful need to be urgently reviewed “The status quo is not an option.”
His successor Jeane Freeman has also called for tighter regulation.
She said: “Doctors, nurses, anaesthetists all have professional regulatory bodies because of the vital — literally life and death — responsibilities they carry.
“They have a professional code to follow.
“We don’t have that for senior, non-clinically qualified executives or managers in the NHS, but they also carry significant responsibilities for patients and patient safety. “We need to look seriously at what might be the comparable approach with this group of very senior NHS staff.”
Following last week’s verdict, the UK Government announced a non-statutory independent inquiry.
READ MORE: Scottish offenders could soon be compelled to come to court
The Scottish Government told The Herald they would be paying close attention to the findings.
A spokesperson said: “Our thoughts and sympathies are with the families affected by these appalling crimes.
“The Scottish Government will work closely with colleagues across the UK to ensure that any learning from the independent review, commissioned by the Department of Health and Social Care, is used to further strengthen protections in our systems if required.”
“It is vital that everyone who works in our Health Service has the confidence to raise any concerns they may have.
“Policy measures are in place to support this and staff should raise a concern with their line manager or team leader, or with a more senior manager if circumstances mean this is more appropriate.
“There are also dedicated whistleblowing champions in each health board to ensure staff are encouraged and supported to speak up.
“The Independent National Whistleblowing Officer, run by the Scottish Public Services Ombudsman, is the first of its kind in the UK and provides a mechanism for external review of how a Health Board, primary care or independent provider has handled a whistleblowing case.”