Smith and Warner were banned from international and domestic cricket for 12 months, while Bancroft was banned for nine. Warner was also banned from holding leadership positions in Australian cricket for life, while Smith and Bancroft were banned from leadership positions for another 12 months after the end of their bans.
"The proposed penalties are disproportionate relative to precedent," ACA president Greg Dyer said in Sydney on Tuesday. "We ask that consideration be given to recalibrating the proposed sanctions, to consider options such as suspending or reducing part of the sanction. To consider allowing the players to return to domestic cricket earlier, for example, as part of their rehabilitation.
"We believe [the bans] are disproportionate. We've pointed out the fact that incidents of this similar type have occurred previously, the sanctions are vastly less than what's been suggested here. There's a need to reconcile between the two, there's a need to understand that disproportionality and to move forward. We're in ongoing conversations with Cricket Australia through this process."
The players have until Thursday to decide whether to appeal the penalties imposed by CA or not.
"The ACA is working strongly with the players," Dyer said. "Their decisions are imminent but I'm not able to share them with you this morning. [It is] a deeply personal decision for the players. We're supporting them through that process but ultimately [whether to appeal is] for the three players to decide."
Dyer was of the opinion that the administration needed to support the banned players during this time, and allowing them to stay involved with cricket would be beneficial. "The players need to be brought back into the confines of the game to be supported by the game - to be assisted by the game, in the rehabilitation," Dyer said. "If the sanctions were to prevent that then I think that would be a bad outcome.
"The loss of leadership is significant as a sanction ... these are very substantial things that have occurred to these men. That needs to be brought into mind. Those [consequences] are over and above the length of the sentence."
Smith, Bancroft and Warner held press conferences after returning to Australia, where they expressed remorse for ball-tampering on the third day of the Newlands Test. All of them were extremely emotional during their press conferences and Dyer said their "extraordinary contrition" should be taken into account by CA.
"The contrition shown by these men is extraordinary. We ask for this extraordinary contrition to be taken into account by Cricket Australia just as it would be in any fair or proper process. Their distressed faces have sent a message across the globe as effective as any sanctions could be. Australia cried with Steve Smith last Thursday. I certainly did. We expect this contrition to be taken into account."