Paine made the explosive claims in his autobiography The Paid Price, with the former Test captain becoming the first player lift the lid on the 2018 Cape Town Test in a tell-all book.
And he says he was stunned and his heart sank as replays showed Bancroft hiding the sandpaper in his pants before being spoken to by umpires.
“I was thinking ‘what the f**k’,” Paine wrote. “A sense of dread came over us all.”
But Paine conceded using sandpaper was “next level” and “shameful”, with traditional tampering usually via means such as throwing the ball into the ground.
Regardless, he says he was left furious when he spotted South Africa allegedly pulling apart the seam of the ball in the following Test.
“I saw it happen in the fourth Test of that series,” Paine wrote. “Think about that. After everything that had happened in Cape Town, after all the headlines and bans and carry on.
“I was standing at the bowlers’ end in the next Test when a shot came up on the screen of a South African player at mid-off having a huge crack at the ball.
“The television director, who had played an active role in catching out Cam, immediately pulled the shot off the screen. We went to the umpires about it, which might seem a bit poor, but we’d been slaughtered and were convinced they’d been up to it since the first Test. But the footage got lost. As it would.”
The wicketkeeper also claimed Warner had every right to be upset after he thought Quinton de Kock had made a comment about his wife Candice before the infamous stairway confrontation in Kingsmead.
“I was the one holding them apart and I know how it unfolded,” Paine said.
Paine has regularly called for Warner’s lifetime leadership ban to be lifted, claiming Cricket Australia seized an opportunity to punish him after the previous year’s pay talks.
And he admitted he felt as if the side had let the opener down before the Cape Town debacle.
“I don’t know how [Warner] kept his cool in those situations and on reflection I feel the team let him down by not offering him more support,” Paine wrote. I can see now he was masking a lot of pain and we should have known it.”
“We suspected that someone had been nurturing the ball too much to get it to reverse so wildly, and we watched the second Test at St George’s through binoculars, so that we could follow the ball more closely while Australia was fielding,” he writes in Faf: Through Fire.
“When we noticed that the ball was going to David Warner quite often – our changing room must have looked like a birdwatching hide as we peered intently through our binoculars.”
The two teams will meet in a Test series for the first time since the 2018-19 encounter when South Africa travel to Australia for three matches in December and January.