"We would encourage both teams to focus their energies on the third test in Ranchi next week," ICC chief executive David Richardson said. "Ahead of that, the match referee will bring both captains together to remind them of their responsibilities to the game.
"We have just witnessed a magnificent game of test cricket, where players from both teams gave their all, and emotions were running high during and after the match."
Smith illegally looked towards the changeroom for advice on whether or not to review an lbw dismissal on Day Four, contritely calling it a "brain fade". Kohli stormed across the pitch and confronted Smith at the time.
Kohli sensationally accused Australia of systematically cheating with regards to the Decision Review System. The unsubstantiated claims were branded "outrageous" by Cricket Australia chief James Sutherland.
The firebrand also straddled the line of dissent, after a failed review in his second innings. Kohli and Cheteshwar Pujara, who has since boasted about sledging David Warner, also targeted many batsmen with non-stop antagonistic verbals.
Both umpires repeatedly talked to Kohli, but tensions never simmered. Mitchell Starc both delivered and received a send-off, while Ajinkya Rahane, Ravichandran Ashwin and Steve O'Keefe were all rebuked by officials during the contest.
"They were talking a lot and probably sledging is something, which, as a unit, we felt that we can give them back," Pujara said, in a video on the website of Board of Control for Cricket in India (BCCI)
"They were always under pressure when they walk into bat. I wanted to make sure their batsmen are thinking about it, especially David Warner.
"Whenever he walks into bat, Ash [Ashwin] is always happy, so I always keep reminding him that Ash is the one [bowler who has dismissed Warner more than any other in Tests]."