he was forced to suspend the four players - Watson, James Pattinson, Mitchell Johnson and Usman Khwaja - because of their unacceptable "back-chat" and "attitude".
"When we sat down as a leadership group and made these tough decisions I knew it would polarise public opinion, but internally I certainly know we've made the absolute right decision.
"This is a line in the sand moment. A point we'll look back on in a couple of years' time when we're back to number one in the world and say was a defining moment," Arthur wrote on the Cricket Australia website.
"Let's be absolutely clear. The decision to suspend Shane Watson, Mitchell Johnson, James Pattinson and Usman Khawaja for not adhering to a team request is the defining moment, but it has been a culmination of lots of small minor indiscretions that have built up to now," he said.
"Being late for a meeting, high skinfolds, wearing the wrong attire, back-chat or giving attitude are just some examples of these behavioural issues that have been addressed discretely but continue to happen," he added.
After two heavy defeats in the opening two Tests of the series against India, Arthur asked all the touring Australian players to prepare a three-point presentation on how they could improve the team's performance and were given five days to submit it, which the quartet failed to deliver resulting in their suspension.
Arthur said the last few days leading to the suspension episode have been the "toughest" phase of his coaching career.
"The last week and a half since the end of the Hyderabad Test has been the toughest in my 11 years of coaching. The media reaction to this decision was like none I've seen in my coaching career and has certainly divided opinion," he said.
The retirements of Ricky Ponting and Mike Hussey had forced Australia to field a relatively young and inexperienced side for the tour of India and Arthur said the team management had provided "lots of latitude and flexibility" keeping that in mind.
"We have given lots of latitude and flexibility with a young and inexperienced squad. We know it's going to take time for them to grow and mature, but there is only so long the leadership group can hold their hand," he said.
"This decision was about sending a strong message that it is about time all players had some accountability for their actions.
"If we're deadly serious about getting back to number one in the world, all players need to raise the bar and lift their game. If not, we must be content at being number three or four or five in world cricket because we won't get any better. The players won't learn and we'll continue a vicious cycle," the South African said.
With Australia due to play two Ashes series against arch-rivals England this year, starting in July, Arthur said the players will have to do away with their attitude problems.
"It is a strong message to everyone in Australian cricket that if you want to play for the Australian Cricket Team, then we demand excellence and corner-cutting, taking short-cuts or arriving with a bad attitude will no longer be tolerated," he said.
"We want to be the Spanish football team, Manchester United or McLaren of world cricket. The absolute pinnacle where high standards are not expected, they are second nature.
"Australian cricket fans deserve nothing less. It is a privilege to wear the Baggy Green," Arthur said.