Sydney (AFP) - Australian media labelled Indian skipper Virat Kohli "classless" and childish on Wednesday after his provocative comments at the end of a hard-fought but incendiary Test series.

Newspapers laid into the winning captain for saying he no longer counted the Australian players as friends, and they also took umbrage at India's apparent snub when invited to join the tourists for a beer.

Kohli said he would not think of the Australians as friends "ever again" after India sealed a 2-1 victory in a pulsating series marked by flare-ups between the world's top two teams.

"Virat Kohli had to shake hands and move on after series win but he acted like a child," read a headline in Sydney's Daily Telegraph, which also called Kohli an "egomaniac".

"Beergate: Kohli's latest classless act", another headline said.

The Australian's Peter Lalor wrote: "If there were any doubts about the poor spirit between the Indian and Australian sides it was confirmed after the series when the home side shunned a suggestion the two sides drink together."

Kohli's behaviour was compared to that of his opposite number Steve Smith, who apologised for calling Murali Vijay a "f***ing cheat" after he claimed a catch when the ball had touched the ground.

"All Virat Kohli had to do was say sorry. Steve Smith did," wrote Herald Sun journalist Russell Gould.

Kohli has repeatedly been a target of the Australian press during the series, to the extent that former captain Michael Clarke warned the criticism was "getting out of control".

Kohli initially stepped into the firing line when he accused Smith of systematically abusing the decision review system, after the Aussie captain admitted looking to his team dressing room when considering whether to appeal his dismissal in Bangalore.

-Smith struck a conciliatory tone at the end of the series, revealing that he reached out to India's stand-in skipper Ajinkya Rahane with the offer of a beer - an invitation that was declined.