Vice-captain Shane Watson, pacers James Pattinson and Mitchell Johnson and batsman Usman Khawaja were left out from the third Test in Mohali, which India won by six wickets.
The four were axed for not completing a presentation on improvements needed in the team on time, a move which was called ridiculous by several former players such as Shane Warne.
The 44-year-old Arthur, who closed his Twitter account today, said he believed the decision was correct as team discipline was important.
"If I'm doing that, I'm not doing my job. I'm empowered to coach this team, to run this team and get this team back to where it needs to be," he asserted.
Arthur said the presence of senior players is very important to develop team spirit.
"We've got to understand where we're at, at the moment, with a very young group of players that needs to be shown the right way to go. If you've got older senior players the team governs itself and then it's easy just to run and coach," he explained.
Arthur, the first foreigner to coach Australia, was roped in for a three-year term when he joined as head coach in November 2011.
Currently lagging 0-3 in the four-match series against India, it is perhaps the toughest phase of Arthur's tenure after decent results with an inexperienced team earlier.
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