New York’s woke mental health system — which refuses to lock up even violent maniacs — is as much to blame for the unprovoked fatal shoving of a retired teacher as the suspect himself, critics told The Post.

“It was the quintessential preventable tragedy,” Carolyn D. Gorman, a fellow at the Manhattan Institute, said Saturday.

“I think there are two issues: There’s a lack of [patient] beds, and there’s a lack of willingness to hold individuals, whether in a locked psychiatric facility … or in a locked jail or prison.

“We have to hold these individuals somewhere. … But if we are not willing to hold them somewhere where they can receive oversight — whether or not they’re receiving treatment at some point — it is a danger not only to the individuals, but to other New Yorkers.”

Rhamell Burke — a 32-year-old serial troublemaker who has been arrested four times since February — walked free from Bellevue Hospital about an hour after cops cuffed him for acting erratically.

Police brought Burke to the facility around 3:30 p.m. Thursday as an “emotionally disturbed person,” they said.

The violent brute was released around 4:40 p.m., and allegedly launched his fatal assault on 76-year-old stranger Ross Falzone at a Chelsea subway station about five hours later, while still sporting his hospital bracelet.

“This horrific case is another example of New York City’s revolving door system failing the public, where dangerous individuals with long criminal histories and severe mental health issues are released right back onto our streets,” said Councilman Phil Wong (D-Queens).

“These are ticking time bombs, and unless we get serious about repeat offenders and involuntary treatment, more innocent New Yorkers will pay the price.”

Mayor Mamdani extended his condolences to the victim’s loved ones on Friday, and called on the city’s hospital system to investigate how the tragedy could have been prevented and to conduct a comprehensive review of its psychiatric evaluation and discharge protocols.

Both Council Speaker Julie Menin and Councilmember Lynn Schulman (D-Queens), who chairs the Committee on Health, on Saturday also called on NYC Health + Hospitals to conduct a thorough probe.

“My heart goes out to the family of Ross Falzone over this senseless death,” said Menin. “NYC Health + Hospitals must conduct a full review of its intake and release of the suspect and make any necessary changes to prevent this kind of tragedy from occurring in the future.”

However, Gorman said it was “distressing” to hear Mamdani’s “very sort of superficial response” to the tragedy, saying an investigation might not even be necessary because the answers are staring him in the face.

“Every New Yorker understands that there are seriously mentally individuals deteriorating on the street, and that this is not a new phenomenon, and yet he has had no interest in addressing serious mental illness in any serious way,” she said.

“This is why [ex-]Mayor [Eric] Adams really wanted to make serious mental illness a focus. Mayor Mamdani is not interested in that whatsoever.”

Mamdani could be reached immediately for comment.