Johnson and Kohli have a history of duels of their own.
Former Australian pacer Mitchell Johnson slammed India captain Virat Kohli, describing his behaviour as "disrespectful" and "silly" during the second Test here.
Kohli and Australia captain Tim Paine were involved in a series of heated exchanges, which at one point prompted umpire Chris Gaffaney to step in to dissolve the tension.
However, once the second Test ended with Australia beating India by 146 runs, both the captains played down the issue, saying no line was crossed.
But Johnson was extremely critical of Kohli's behaviour during the Test.
"At the end of the match, you should be able to look each other in the eyes, shake hands and say 'great contest'," he wrote in a column for Fox Sports.
"Virat Kohli could not do that with Tim Paine, shaking the Australian captain's hand but barely making eye contact with him. To me, that is disrespectful.
"Kohli gets away with more than most cricketers simply because he is Virat Kohli and he gets placed on a pedestal but this Test left the Indian captain looking silly," he wrote.
BCCI on Tuesday came out in support of Kohli, rubbishing media reports in Australia which claimed that Kohli had bragged about being the best batsman in the world while ridiculing Paine as a "stand-in captain".
Johnson said that Kohli didn't his keep words after making pre-series claims that he won't initiate any confrontations.
"Kohli has contradicted the things he said at the start of the series. He said he was a changed person - that he was coming in with a different attitude to last time and wasn't going to initiate anything. What we saw this Test says otherwise," he wrote.
"From my experiences with him and what I am seeing as an observer now, not much has changed. It was disappointing and that is not the only area where he let himself down."
Kohli scored a sparkling 123 in the first innings before being dismissed in a controversial fashion following a contentious catch at slip by Peter Handscomb.
Johnson was offended with Kohli for not acknowledging the standing ovation at Perth stadium after his dismissal.
"To me, the catch was given out so you accept it and move on and as a player who has scored a hundred you acknowledge the standing ovation," he said.
Johnson and Kohli had a fiery relationship after the 2014 Melbourne Test where the pacer's throw had hit Kohli during his attempt to get the batsman run out.
