Cricket Australia's (CA) board on Tuesday held a teleconference with its management to take a briefing following Monday's events in Mohali.
The Australian team management on Monday dropped vice-captain Shane Watson, James Pattinson, Usman Khawaja and Mitchell Johnson for the third Test against India for breach of discipline.
CA chairman Wally Edwards said: "We had a discussion so we could be fully updated on the issues surrounding this event and allow board members to ask questions of the management. The board is completely supportive of the actions taken by team management."
The dropped players were given five days to submit three points on what they bring to the team either by mail or in person. But the four players failed to meet the deadline.
Following the management's decision, Watson packed his bags and left for home, saying he needed to be with his pregnant wife Lee. Watson and his wife are expecting their first child later this month.
Watson, 31, said he is also weighing his future in Test cricket.