"Our group are under no illusions; we've got to keep working really hard and keep improving", Australian captain Tim Paine.
The hosts Australia was bundled out for 300 on the fourth day, which also forced them to follow-on at home for the first time in 30 years.
At the post-match presentation, Kohli termed the series win as a stepping stone for greater things to come. "We had our chances in Adelaide, and in Perth I thought we played some good cricket, but in Melbourne and Sydney, we've been outplayed".
"It felt good, it was very easy, but Pujara couldn't even do that", Kohli said with a smile.
India were the favourites to lift the trophy but a 147-run loss in the second Test match raised some doubts.
For some Australians the series will always carry an asterisk given their two best batsmen, Steve Smith and David Warner, were unavailable because of bans they received for the ball-tampering scandal in South Africa a year ago.
And us? We'll know more after the upcoming two-Test series against Sri Lanka, which for the record is the fifth versus sixth battle on current Test rankings.
"And all the struggles that we have gone through in the past 12 months as well as the team".
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The tourists, led by magnificent series from batting rock Cheteshwar Pujara and superb slinger Jasprit Bumrah, achieved it in clinical fashion to expose the huge void left by Steve Smith and David Warner's suspensions and raise questions about the potency of Australia's attack.
The Indian coach also ties a common thread to two earlier, perhaps most-defining triumphs in the history of Indian cricket - the 1983 World Cup, and the 1985 World Championship - having been part of both those squads. Mitchell Starc is trying his absolute best to do the same thing he did a year ago when he was swinging the ball around corners.
"That's how you win Test matches". We put everything on the line to win for the team. "We are the 12th man of "Team India", so we'll be celebrating with them, and then the party will go on", Rajul Sharma, who heads up the Australian branch of Bharat Army, told AFP.
"We want to do the best for Indian cricket, and this is outstanding, but it's just a stepping stone".
In his congratulatory message to the side, President Kovind lauded the effort in achieving the series win.
India thrashed Sri Lanka by an innings and 171 runs in the third and final Test at the Pallekele International Stadium to complete a historic 3-0 clean sweep of an overseas Test series.
"We definitely want to build on this and always promote the message of Test cricket being the most important and the most valued format of the game which it rightfully is".
But another Pujara century in Melbourne set the visitors up for a big first innings total and when Australia capitulated in reply to 151 all out, the scene was set for India to take a stranglehold on the series coming into Sydney.