With out-of-form skipper Rohit missing, the visitors went down by six wickets in the fifth and final Test on Sunday in Sydney to lose the series 3-1.
Fresh from a 3-0 home whitewash to New Zealand, the defeat sparked renewed debate in India about the future of the team and in particular two of its stalwarts.
The 37-year-old opening batsman Rohit, who missed the only India win of the series in the first Test because of the birth of his second child, managed 31 runs in three matches.
Kohli, 36, scored an unbeaten century in the first Test but otherwise had another underwhelming series by his sky-high standards.
Australia booked a meeting with South Africa in the World Test Championship final in June, after India lost out in the race with six Test losses in eight matches.
India's next Test assignment is their tour to England in June-July, when the visitors will play five matches and selectors will have to make a call on Kohli and Rohit.
"I think the next 8–10 days are crucial for Indian cricket to take a good, honest look at itself," former captain Sunil Gavaskar told news channel India Today.
"Most importantly, the star culture has to end. Total commitment to Indian cricket is non-negotiable.
"We don't need players who are partly here and partly elsewhere. It's time to stop pampering anyone."
Kohli skipped matches after the birth of his second child in February last year.
Apart from his century, Kohli scored 90 runs across eight innings.
Dubbed "King Kohli" for his prolific scoring, the batsman averaged above 54 before 2019, but from 2020 onwards his average has slipped to 30.72.
Kohli and Rohit have been criticised for not participating in domestic matches to improve their faltering form, a decision that irked many pundits including Gavaskar.
"The cricket board needs to stop acting like admirers and put their foot down," the batting great said.
"They must tell the players that Indian cricket comes first. It's either a full commitment to Indian cricket or other priorities."'Up to them'
Rohit, who had also been censured for his decision-making as skipper, said it was his choice to stand down for the decisive fifth Test.
He also insisted he was not retiring.
Former India batsman Sanjay Manjrekar did not mince his words.
"When to retire is up to the player," he wrote on social media.
"But how long to play is up to the selectors."
Jasprit Bumrah, the vice captain, would be the clear pick to replace Rohit as Test captain after the pace spearhead took 32 wickets in five Tests in Australia and led the team to victory in the first match in Perth.
Coach Gautam Gambhir, who received flak for keeping the media guessing in his pre-match press conference about whether Rohit would play in Sydney, appears to favour keeping the duo at his disposal.
"I can't talk about the future of any player. It's up to them as well," Gambhir said.
"They still have the hunger, they still have the passion, they are tough people and hopefully they can continue to take Indian cricket forward."
He added: "Whatever they plan, they will plan in the best interest of the team."
Kohli and Rohit both called time on their T20 international careers last year soon after India won the World Cup in June.
Both are expected to play in the one-day Champions Trophy in Dubai and Pakistan in February-March.
