(CNN) The former Navy SEAL who says he fired the shot that killed Osama bin Laden says he doesn't care if people believe him.

"The most important thing that I've learned in the last two years is to me it doesn't matter anymore if I am 'The Shooter.' The team got him," Robert O'Neill said in an audio interview with freelance journalist Alex Quade, a former CNN correspondent, that aired Friday on CNN's "AC360."

"Regardless of the negativity that comes with it, I don't give a f***. We got him."

"AC360" obtained the audio interview from Quade, who conducted a series of interviews with O'Neill over the past 18 months.

The killing of bin Laden will go down in history, O'Neill said. "But I don't care if I'm 'The Shooter,' and there are people who think I'm not. So whatever."

The audio interview follows an interview published this week in The Washington Post, in which O'Neill publicly identified himself as the SEAL who killed the leader of al Qaeda in 2011.

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The 38-year-old O'Neill had previously revealed details of the mission to Esquire magazine. But he was hesitant to attach his name to the account until his identity was linked to the story on a military blog earlier this week without his consent.

O'Neill told the Post that other SEAL team members were involved in the raid, including Matt Bissonnette, who detailed the group's experiences in his memoir, "No Easy Day," written under the pseudonym Mark Owen.

O'Neill, who had been serving as a SEAL for 15 years at the time of the bin Laden raid, had participated in other missions, but he said he feared this mission would be his most difficult.

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In the audio interview with Quade, he said the members of SEAL Team Six talked about the September 11, 2001, terror attacks. He and other team members believed they would not return alive from the mission to get bin Laden.

"Well, you have to go pump yourself up to go die. So we would talk about this," O'Neill said.

"...(It was a) group of guys who knew time on Earth was up, so you could be honest with each other. And we all accepted and nobody was afraid. It was really cool."

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He also said when he identified himself as the shooter to the families of 9/11 victims, they thanked him for closure.

"He died afraid, and he knew we were there to kill him. And that's closure," he said in the audio interview.

O'Neill's move to go public is a controversial one, as it violates an unspoken military rule: Don't seek attention for your service.

"We do not abide willful or selfish disregard for our core values in return for public notoriety or financial gain," said an October 31 letter to the Naval Special Warfare ranks from commanding officer B.L. Losey and force Master Sgt. M.L. Margaraci.

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In the audio interview, O'Neill says he believes some details about the bin Laden mission, such as how he was killed, were no longer classified because they had been repeatedly leaked in the aftermath by high-level officials.

"Once anyone says anything at that level, it's not classified," he said.

"...I was told by people that I can't even say I'm a Navy SEAL, so I don't give a f*** what they think."

Twenty-three SEALs and their interpreter launched the assault on the bin Laden compound just after midnight on the morning of May 2, 2011. They shot and killed bin Laden's two bodyguards, one of bin Laden's sons and the wife of one of the bodyguards. They also wounded two other women.

O'Neill has told his story before in a lengthy profile in Esquire in 2013, in which O'Neill was described not with his real name but only as "The Shooter."

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In the Esquire piece, O'Neill/The Shooter was said to have encountered al Qaeda's leader face-to-face in the top-floor bedroom of the compound in Abbottabad where he had been hiding for more than five years.

The Shooter said the al Qaeda leader was standing up and had a gun "within reach," and it was only then that the Shooter fired two shots into bin Laden's forehead, killing him. That account was in conflict with the narrative in "No Easy Day."

Another member of the secretive SEAL Team 6, which executed the bin Laden raid, told CNN's Peter Bergen the story of The Shooter as presented in Esquire is false. According to this serving SEAL Team 6 operator, the story is "complete BS."

But in the audio interview, O'Neill dismissed the criticism.

"Even now, I mean, there are guys now saying that I am full of s***," he said. "...You only know what you were told unless you were in the room. And unfortunately for me, there was two people in the room, and one of us is dead and that's Osama bin Laden."