Warner also says he's been given a "life punishment" for his role in the sandpaper scandal as a rift in Australian cricket deepens.
"For me, it's about accepting the truth, and I just don't think this will rest," Warner told Fox Cricket on Friday.
"I'm still getting called the architect, the fixer, and all this kind of stuff - and it really, really hurts.
"But it's also affected ... the Australian cricket team.
"So it's important for us to allow us time to heal it, but until the truth is accepted, it's going to be very, very difficult to move on."
Warner was disheartened at Cummins' lengthy media conference earlier Friday when the skipper again rejected knowledge of plans to use sandpaper on the ball in the infamous Test against South Africa in Cape Town in 2018.
Warner said he stood by Khawaja's claims in his book that the entire team knew of the sandpaper plot.
"I still stick by Uzzy and what he's written in that book. It's the truth and I really, really support him," Warner said.
"I actually feel for him at the moment.
"I actually feel that the captain today actually threw Uzzy under the bus and I'm very, very disappointed about that."
Warner and Steve Smith were banned from cricket for 12 months, and stripped of the Test vice-captaincy and captaincy respectively, for their roles in Australia's use of sandpaper on the ball in the Cape Town match.
Cameron Bancroft, who was busted by television cameras with the sandpaper, was suspended for nine months by Cricket Australia (CA).
"All three of us have paid a big price in this - and I hadn't spoken about it in eight years," Warner said.
"But at the end of the day, we've got to live with these consequences daily, and we've been served a life punishment.
"So when other people talk about they have been affected by it, there's no nothing worse for me, Steven, Cameron, who have to walk out there every single day, and we cop abuse.
"Yes, we accepted it.
"But at the end of the day, my wife and I as well paid the greatest price, we lost a baby during that time, and that's why it really hurts me the most until the truth is accepted."
Warner said CA had performed a "botched investigation" into the Cape Town flashpoint.
"It was a quick one to get it over and done with. Some of the questions were quite challenging in a way that it was being planted on us.
"And then we had to move on and just accept responsibility for three of us, and we ultimately did."
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