Cricket Australia boss James Sutherland says national team management, including Mickey Arthur, John Inverarity and Pat Howard, retains the board's full support but agrees the 4-0 defeat in India is "not acceptable."
According to Sydney Morning Herald, Arthur, in the job since November 2011, is under contract with CA until the end of the next World Cup, to be held in Australia in 2015, but is under pressure after presiding over the country's heaviest loss in a series in 34 years.
Arthur's lead role in the suspension of four players -Shane Watson, James Pattinson, Mitchell Johnson and Usman Khawaja - for the third Test in Mohali was also heavily criticised, although he explained it as a necessary move to correct a slipping team culture.
High-performance manager Howard, a former Wallabies rugby international, was another under fire during the Indian tour, particularly when he questioned Watson's commitment to the team and alluded to "issues" in the relationship between the vice-captain and captain Michael Clarke.
"Like the fans and the players, we are all disappointed with our performances in India," he said.
"We always knew the conditions would be uniquely tough and we went to India with a team that is young and relatively inexperienced by current international cricket comparison. But it is not acceptable to either Australian cricket fans or to any of us involved to lose so convincingly."
"While the group has had a difficult month, its resolve has never been higher and I know we will bounce back."
The CA chief executive said the board continued to back the tough stance taken by Arthur, Clarke and team manager Gavin Dovey in Mohali. But he admitted there were "issues to assess".
"Our last board meeting took a detailed presentation on team performance plans as we move through the current transition period and endorsed the approach Pat Howard, Michael Clarke, Mickey Arthur and the selectors are taking as we identify, develop and blood the next generation of talent," Sutherland said.