Former skipper Smith and vice-captain Warner were banned for a year, and Bancroft for nine months after Cricket Australia (CA) held them guilty of conspiring to "change the condition of the ball" in last week's third test against South Africa.
The case caused public outrage in Australia but the sentences have been criticised in some quarters as being disproportionately harsh, including by former Australian spin bowler Shane Warne.
The ACA, which represents professional first-class cricketers, called for a proposed review into Australia's cricketing culture to be fully independent and extend to the CA's response to the scandal.
"There are a number of glaring and clear anomalies in the process to date which causes the ACA to query the severity and proportionality of the proposed sanctions," the organisation said in a statement on Thursday.
Listing the anomalies, the ACA pointed out that the bans imposed by CA were considerably lengthier than any that the world governing body (ICC) had handed down in the past for similar offences.
It also questioned why CA's public statements had not referenced contextual factors "including the environment in South Africa during the series" and criticised the rush to put the players before the media without considered and coherent advice.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)