Peever's comments, which could be construed as a crack at India, came a day after Indian skipper Virat Kohli declared his friendships with the Australian players over, after a series boasting wonderful cricket was marred by heated verbal exchanges.

"There were many fine individual performances, but none better than those of the captain. Steve showed yet again what an outstanding leader he is becoming, and his honesty and gracious comments at the end demonstrated the qualities that Australians expect from their Test captain," Peever said.

"It was a tough series, as we expected and, indeed, welcome from our Indian hosts. Cricket at this level is highly competitive and it is incumbent on all involved, players and administrators, to honour the protocols and standards of behaviour that underpin the spirit of cricket."

It is rare, almost unheard of, for a CA chairman to release a statement after a Test series, but such were the tensions between the two camps in this four-Test campaign that Peever opted to express his feelings.

Tensions exploded after India evened the series in the second Test, when Kohli claimed Smith had "crossed the line" by trying to get help from his dressing room with the decision review system.

He also made unsubstantiated claims the tourists had repeated this throughout the game. Smith later described his actions as "a bit of a brain-fade".

CA chief James Sutherland slammed Kohli's team claim as "outrageous", with the Board of Control for Cricket in India insisting Kohli's comments and conduct had been "exemplary".

CA and the BCCI were later forced to make peace.

The friction returned in the drawn third Test when Kohli injured his shoulder diving to save a boundary, and Australian Glenn Maxwell was accused of mocking him later in the match.

Kohli had declared before the series that he was "really good friends with all these [Australian] guys off the field", but after India's eight-wicket win in Dharamsala, which clinched the 2-1 series win, he said: "No, it has changed. You won't hear me say that ever again."

The tourists were also disappointed with several incidents, notably the decision by the BCCI to allow video of an on-field spat between Ravindra Jadeja and Matthew Wade to be posted.

"As the team arrives home over the next two days, they will find that all of Australia is immensely proud of their efforts," Peever said.

"Some gave them little chance of testing the world's No.1 team, but instead they showed resilience, adaptability and a determination to overcome the difficulties they have experienced in recent years in such conditions. They came very close to winning the series, but did achieve Australia's first Test win in India since 2004."

World champions a year ago, Australia have slipped to No.3 in the Test rankings. There is a slated short tour of Bangladesh to come in August, before a home Ashes campaign from November.

Peever said Cricket Australia was determined to have the team winning again on the road.

"As a result of this series, and the series just completed in New Zealand, Australia has finished as the No.3-ranked Test team for this international season," he said.

"We aspire to be No.1 in all formats, so while the team's efforts in India, and across the summer following the disappointment of the first two Tests against South Africa, represent a significant improvement, we all know that we must continue to learn and develop our skills.

"We want to win major trophies like the Ashes and the Border Gavaskar, not just at home but overseas as well."