SYDNEY (Reuters) - Australia have done themselves proud with their spirited fight in India but must continue to improve to become the number one side across all formats, the country's cricket board said on Wednesday.
Last year, Australia suffered a 3-0 whitewash in Sri Lanka before Steve Smith's men were beaten at home in the first two tests by South Africa.
An overhauled side gained a consolation win against the Proteas in a day-nighter at Adelaide Oval to lose the series 2-1 and then hammered visiting Pakistan 3-0.
As they headed off for the four-match series in India many, including former test off-spinner Harbhajan Singh, predicted a repeat of the 4-0 whitewash they suffered in 2013.
Smith's side, however, won the series opener in Pune before losing from a strong position in Bangalore and eking out a draw in Ranchi to set up a winner-takes-all decider in Dharamsala.
A second innings slump then helped India to a eight-wicket win for a 2-1 series triumph on Tuesday but Australia's efforts earned them widespread praise.
"As the team arrives home over the next two days, they will find that all of Australia is immensely proud of their efforts," Cricket Australia chairman David Peever said in a statement.
"Some gave them little chance of testing the world's number one team, but instead showed resilience, adaptability and a determination to overcome the difficulties they have experienced in recent years in such conditions."
With the series loss, Australia will finish the season ranked number three behind India and South Africa in tests.
"We aspire to be number one 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," Peever said.
"We want to win major trophies, like the Ashes and the Border-Gavaskar, not just at home but overseas as well."
Australia's 333-run victory in the series opener in Pune was their first in India since 2004 and also halted the hosts' unbeaten run of 19 tests.
Smith scored a century in that match to set up the win and also finished as the highest run-getter in the series with 499 runs, including two more hundreds.
"There were many fine individual performances, but none better than those of the captain," Peever said.
"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."
The hard-fought series also ended with plenty of acrimony on the field with India captain Virat Kohli declaring that his friendship with Australia's cricketers was over.
Kohli had criticised counterpart Smith, who acknowledged he had a 'brain fade' in the second test in Bengaluru when he gestured to the dressing room seeking guidance on whether to review an umpiring decision.
It needed a meeting between the two cricket boards to calm things down before the third test in Ranchi.
"It was a tough series, as we expected and indeed welcome from our Indian hosts," Peever said.
"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."
(Reporting by Sudipto Ganguly in Mumbai; editing by Nick Mulvenney)