The Board of Control for Cricket in India has asked the International Cricket Council to look at Australia captain Steve Smith's "brain fade" admission on the concluding day of the second Test in Bangalore.

India skipper Kohli was careful not to use the word 'cheating' after India sealed a series-levelling 75-run win on Tuesday, but left no doubt that he felt Smith had crossed the line by seeking off-field advice for a decision review system referral.

Cricket Australia chief executive James Sutherland released a statement earlier on Wednesday in which he labelled Kohli's criticism "outrageous".

The BCCI then issued a statement of its own in which it backed Kohli and the India team, and called for Smith's remark to be examined.

"The Board of Control for Cricket in India, after due deliberation and seeing the video replays of the episode, steadfastly stands with the Indian cricket team and its captain Mr Virat Kohli," the statement read.

"Mr Virat Kohli is a mature and seasoned cricketer and his conduct on the field has been exemplary. Mr Kohli's action was supported by ICC elite panel umpire Mr Nigel Llong, who rushed in to dissuade Mr Steve Smith from taking recourse to inappropriate assistance.

"BCCI has requested the ICC to take cognizance of the fact that the Australian skipper Mr Steve Smith in his press conference admitted to a 'brain fade' at that moment.

"BCCI sincerely hopes that the rest of the matches are played in the true spirit of cricket."

Kohli was less than impressed with Smith's antics (Getty)

Smith did clearly look towards the dressing room, seeking advice on whether to refer an lbw decision.

The umpires spotted this and intervened, but that did not stop Kohli approaching Smith and offering his own unadulterated thoughts on the subject.

Speaking before Kohli's comments on Tuesday, Smith described his actions in the middle as little more than absent-mindedness.

"I got hit on the pad and looked down to Petey (Handscomb) and he said look up there," Smith said.

"So I turned around and it was a bit of a brain fade on my behalf. I shouldn't have done that. I was looking at our boys, so shouldn't have done that and it was a bit of a brain fade."

Kohli was careful not to accuse Smith of 'cheating' (Getty)

Kohli gave that explanation short shrift.

"Honestly, if someone makes a mistake while batting, for me, personally, that's a brain fade," he said.

"But if something is going on for three days, then that's not a brain fade, as simple as that. I don't want to say more on that, videos are out there for everyone to see. It was getting repetitive."

Kohli and Smith were involved in a heated dispute (Getty)

Sutherland earlier on Wednesday defended his men, saying in a statement: "I find the allegations questioning the integrity of Steve Smith, the Australian team and the dressing room, outrageous.

"Steve is an outstanding cricketer and person, and role model to many aspiring cricketers and we have every faith that there was no ill-intent in his actions.

"We reject any commentary that suggests our integrity was brought into disrepute or that systemic unfair tactics are used, and stand by Steve and the Australian cricketers who are proudly representing our country."

Speaking at the post-match press conference, Kohli said India have observed Australian players looking off-field for help on reviews - which is not allowed under current match conditions around DRS - on several occasions and were no longer willing to tolerate it.

"When he (Smith) turned back the umpire knew exactly what was going on, because we observed that, we told the match referee also, and the umpires, that they've been doing that for the last three days and this has to stop," a visibly riled Kohli said.

"There's a line that you don't cross on the cricket field, because sledging and playing against the opponents is different, but... I don't want to mention the word, but it falls in that bracket. I would never do something like that on the cricket field."