Matthews, a board member for the Australian Cricketers Association focusing on retired players' futures, said he was shocked at how little past Test players had done to better cricket's deteriorating culture.
Smith and Warner are now serving a one-year ban while Bancroft was sanctioned for nine months for the ball-tampering scandal in March.
As revealed by The Daily Telegraph, the Australian Cricketers Association is poised to make an official submission to the Cricket Australia board to try and reduce the ball-tampering penalties on the basis that they're disproportionate to the lack of responsibility taken by CA administrators.
The new maximum ban for ball-tampering, enacted after the incident in South Africa, to a maximum six Tests.
"There was a full investigation, and that was the outcome", Peever said.
"We've got start rebuilding the cricket team to start winning games for Australia and get a cricket team that Australia can be proud of".
A "win at all costs" culture was said to have infiltrated the game, culminating in the ball-tampering fiasco in South Africa in March.
"Over recent years, David Warner and Steve Smith have attracted the highest number of Code of Conduct breaches for worldwide matches", the review said.
The justice meted out to the disgraced trio is hardly mentioned by The Ethics Centre in its 145-page summary of the sorry state of Australian cricket.
"The most common description of CA is as "arrogant" and "controlling", the report said.
He likened cricket's relentless pursuit of victory to the Australian banking sector's drive for excessive profits, which has led to revelations that dead people were charged for services that were never provided.
"It details a corporate culture which is as bad as I've seen in 30 years in the corporate world", he said. "I know that Smith will be passionate, he's still only young, he loves cricket and he's got that drive to get back there".
CA's Pat Howard and Ian Roy completed a formal investigation into the sandpaper saga in two days.
Lehmann, who stood down as Australian head coach shortly after the scandal, now believes Cricket Australia should consider shortening the bans to Smith, Warner and Bancroft.
Asked why so few players took part, Nicholson said some may have given their feedback to the ACA, who then contributed to the review, rather than address the survey directly.
They have rejected a recommendation to allow players to not participate in Twenty20 cricket, however.
"They gave us a lot of feedback around that and that came through the overall Longstaff report", Nicholson said.