Chasing 106 on the penultimate day of the fourth Test, opener Lokesh Rahul hit 51 not out at India's newest Test venue as the hosts seized back the Border-Gavaskar trophy from Australia.
India's stand-in skipper Ajinkya Rahane (38 not out) hit two sixes in a row off paceman Pat Cummins en route to the team's seventh successive Test series victory, a run that kicked off with their triumph in Sri Lanka in 2015.
But Kohli, who sat out the final Test with a shoulder injury, said any warm feelings he had toward Australia before the Test had evaporated during the bitter contest that ensued between the world's top two sides.
"I thought that was the case, but it has changed for sure. As I said in the heat of the battle, you want to be competitive but yeah I have been proven wrong," Kohli told a post-match press conference.
"The thing I said before the first Test (about being friends), I have certainly been proven wrong, and you won't hear me say that ever again."
The 28-year-old skipper caused a furore in the second Test after accusing his counterpart Steven Smith of repeatedly abusing the decision review system.
But Kohli, who managed only 46 runs in the series, said the hard-fought series against Australia was the most satisfying of India's recent run, that included victories over New Zealand, England and Bangladesh in an extended home season.
"Unbelievable. This is the best series win so far," said Kohli, who received the Test mace on behalf of India for ending the season as the world's top side.
"The way the Australian team gave us a fight was really amazing, but the way the (India) guys kept bouncing back showed the true character of the side."
India's cricket board rewarded their players who featured in all four Tests with a cash bonanza of $77,000.
Smith meanwhile apologised for letting emotions get the better of him. On Monday footage indicated he called Murali Vijay a "cheat" for wrongly claiming a catch.
"I have been pretty intense throughout this series. I really wanted to do well for the team. At times I have been in my own bubble and have let my emotions slip. I apologise for that," said Smith.
In the maiden Test played in Dharamsala, India scored 332 in their first innings in reply to Australia's 300, before the tourists collapsed for just 137 on the third day.
On day four, India lost Vijay to fast bowler Pat Cummins and Cheteshwar Pujara to a run out. But these were the only scares for the hosts, who reached their target in less than 24 overs.
The main architect of India's victory was all-rounder Ravindra Jadeja, who was named man of the match and series for his exceptional performance.
He top-scored with 63 in the first innings before taking three wickets with his left-arm spin during Australia's second knock.
"The way the guys handled situations and the way Ajinkya led was outstanding," Kohli said.
"But the maturity and the responsibility shown by all the guys in the team was pleasing to see," he added.
Kohli's own behaviour was parodied in the Australian media, some of whom disparagingly compared him to US President Donald Trump.
The contest will also be remembered for the fine form of Aussie captain Smith, who amassed 499 runs with three centuries, becoming only the sixth visiting batsman to hit as many hundreds.