Shane Watson, Mitchell Johnson, James Pattinson and Usman Khawaja were suspended for failing to respond to a request from management to suggest ways to improve the Australia team.
"If you asked me whether I believed in what we did and whether we would make that decision again, yes we would," South African Arthur told the BBC.
Vice-captain Watson returned to Australia following the decision to be with his pregnant wife, although that was always planned.
He has now returned to India, however, and could lead Australia in the fourth Test because captain Michael Clarke has a back injury.
"Shane's the vice-captain for this tour but we'll wait to see how it pans out," Arthur said.
"He has reflected on what happened and what he did, and just wants to move on now."
Australia, who play England in back-to-back Ashes series later this year, lost the first three Tests in India and Arthur said the decision to drop the four players was the toughest of his coaching career.
"I've reflected long and hard because it's been a really tough 12 days - probably the toughest ever of my coaching career," he said.
"What we've got is a team of inexperienced but very talented young players and our leadership style had to change towards them.
"We had to demand excellence. We could sit and wallow in mediocrity and stay third or fourth in the world.
"Or we could take a paradigm shift in everything we did - put the team first, be ruthless on team etiquette and basics and give ourselves the best possible chance of winning the Ashes and getting back to number one in the world."
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- Shane Watson