Other players involved in the Cape Town controversy have repeatedly denied involvement or knowledge of the plot to alter the condition of the ball by rubbing it with sandpaper.
Four bowlers who played for Australia in that Test - Pat Cummins, Mitchell Starc, Josh Hazlewood and Nathan Lyon - remain part of the team. Cummins has been Test captain since 2021.
In 2021, the quartet released a joint statement which said they "did not know a foreign substance was taken on to the field".
On Saturday, Darren Lehmann, the Australia coach who resigned in the wake of the ball-tampering scandal, also denied Khawaja's claims when he told ABC: "I don't think everyone would have known."
Khawaja retired from international cricket in January. He scored 6,229 runs in 88 Tests for Australia.
In October, it was revealed that Khawaja had met with Cummins to discuss the contents of the upcoming autobiography.
That meeting took place before Australia's recent Test series in South Africa, which the Proteas won 2-1.
In the videos on Instagram, 39-year-old Khawaja explained that blame for the plot should have been shared among the entire set-up, not only Smith, Warner and Bancroft.
"I waited till the [South Africa] series was over. And you know what? I haven't thrown anyone under the bus," Khawaja said.
"The guys that are currently in the team right now and the other people that were there on the South African tour, including me, we're not the victims.
"These three guys took the blame for all of us, and they're the victims. Yes, it was tough for everyone, including me. I had sleepless nights, too."
Khawaja also defended not revealing his version of the sandpaper saga at the time, or following the bowlers' statement in 2021, and instead waiting for his autobiography.
"You ask why didn't I say anything in those four years after that while I was still playing? You know what? I never wanted to be the first guy to chat about this," he said.
"Call me a chicken or whatever you want, I didn't know how to do it because I was still on the team. How was I ever supposed to bring this up when I knew some of my team-mates didn't want to talk about it?"
Cricket Australia is yet to indicate a desire to re-open the investigation into the events at Newlands in 2018.
A statement from the governing body said: "There has been a great deal of speculation in the eight years since the 2018 Cape Town Test, including extensive media coverage throughout last month's series in South Africa.
"During this time there has been the ongoing opportunity to present any relevant information, and this remains the case. All relevant information presented to CA to date has been properly considered and we remain comfortable with the findings of our integrity process."
