FDNY brass read the riot act to firefighters at the Midtown firehouse where an African-American rookie claimed he was hazed by naked smoke-eaters — calling the reported incident “a sexual assault” and a “cover up,” bombshell audiotapes obtained by The Post reveal.

The officers warned the members of Ladder 35/Engine 40 — nicknamed “The Cavemen” — that “if this gets out to the media, there are guys gonna lose their jobs.”

One fed-up officer barked, “We’re not ‘Animal House.’ ”

The closed-door meeting in the kitchen of the Lincoln Center firehouse took place on Dec. 9, 2015, about two months after probationary firefighter Gordon Springs filed federal and city complaints about his alleged sexual hazing there.

Springs, 27, claims that on his first day at the firehouse on May 4, 2015, he and three other rookies were humiliated by a gang of naked firemen in the weight room. He claimed one firefighter dangled his genitals onto his face while he was prone on a bench.

Last October, seven firefighters were disciplined in the case, but none were fired. The FDNY said it consulted with the city Department of Investigation, and has never acknowledged a crime was committed.

But during the secretly taped meeting attended by a lieutenant, a captain and a chief, one of the FDNY bosses clearly raises the issue of criminality.

“I understand the majority of this is bulls–t . . . But what was reported that happened, on the more than one instances for the hazing, it is sexual assault, all right?” an officer says.

A second boss demands an end to the “cover-up.”

“I can honestly tell you the cover-up is worse than the crime . . . Do not cover up. It’s not a secret. And the cover-up is not going to work.”

The officers refer to an internal investigation of “several” hazing incidents.

“There was another incident which was almost taken care of but more information came” out, says one boss.

A source said the meeting came a day after a physical altercation at the firehouse.

On the tape, the officers repeatedly order all hazing to stop.

‘I can honestly tell you the cover-up is worse than the crime . . . Do not cover up. It’s not a secret. And the cover-up is not going to work.’

“All the bulls–t, it has to f–king stop,” demands one officer. “This little game we’ve been playing in the firehouse has run its course. This is serious s–t. We’re in a tough spot here.”

They also counsel the firefighters to be “honest” with the FDNY’s Bureau of Investigations and Trials (BITS), which was looking into the case along with the agency’s Equal Employment Opportunity office.

One officer says the EEO “wants us to be done with it. They’re doing everything they can. They’re gonna work with us.”

But they also warn that “the administration” might want “you f–king fired, all right?”

Springs last month filed a lawsuit in Manhattan federal court against the city, Fire Commissioner Daniel Nigro, a lieutenant and three firefighters, charging sexual abuse and racial discrimination.

The tapes “shock the conscience,” Springs’ lawyer, Paul Liggieri, told The Post. “Time and time again FDNY representatives labeled this incident as ‘hazing,’ but this time around we got to hear the truth from the horse’s mouth. It was a sexual assault.”

Liggieri blasted the DOI, which didn’t question Springs, for its incomplete probe.

“I call upon the DOI to further investigate the matter and to interview my client,” he said. “If investigations start and stop with the FDNY, we are allowing the fox to guard the hen house.”

The DOI and FDNY declined to comment.

At the end of the Dec. 9 firehouse huddle, an officer adds, “We just want to get this over with, get 35 and 40 off the radar, and move on, and let them pick on somebody somewhere else.”