One of the images of the day was of Kohli, 36, storming Constance after the Australian had beaten the Indian bowlers around the ground.
Kohli appeared to change direction to connect with Konstas, who was walking down the field to talk to his opening batting partner Khawaja.
Speaking to host broadcaster Seven Network, former Australia captain Ricky Ponting said Kohli may be to blame.
“This guy (Kohli) might have some questions to answer,” Ponting said.
“When you're out there batting, the batsman owns the wicket. The crease is his king. Especially between overs like that.”
The International Cricket Council can ban players for “inappropriate physical contact” if deemed serious enough, although it is not yet clear whether either player will face any further action.
The incident summed up what was set to be a disciplinary day for India, who were visibly frustrated with the Australian top order collectively taking shape.
But that late burst of wickets, led by the irrepressible Bumrah, brought the visitors back into the game.
Labuschagne looked well placed to reach three figures before pacer Washington Sundar, who was recalled in place of Shubman Gill, attacked the ball straight to Kohli at mid-off.
Travis Head, who had scored two centuries in his previous three innings, departed for a duck after carrying his arms to a Bumrah delivery that was flung back and clipped the top of his off-stump.
Two overs later, Marsh tried to break through the line but could only get to Carey to take Bumrah's third wicket of the day and the 24th over of the series.
Depp then made the most of a late surge with the new ball with the beauty of a feathered edge delivery from Carey.