"I don't want to curb any natural instinct of the players as long as they go out there and do what is expected of them. I don't think we need to read too much into the aggression. Every player has his own way of having a game face," Kumble said ahead of the third Test.
The big-ticket series is poised at 1-1, with everything to play for in the remaining two matches.
The DRS controversy surrounding Steve Smith's dismissal threatened to overshadow India's fightback, eventually prompting BCCI and Cricket Australia to issue a joint statement to bring the matter to an end.
"As custodians of this great game, we believe it's important that we look after the game. Key stakeholders are the players and they certainly understand their responsibility," the former India captain told reporters.
"I think what was important was to focus back on the game. I am very glad the BCCI took a very matured call with Cricket Australia and issued a joint statement that cricket needs to move on and moved out from whatever happened in Bangalore.
"That I think is important because focus has to be on the game. I thought we made a really fantastic comeback after losing the first Test. It was very rewarding," he said.
Asked if Smith and Virat Kohli would meet before the town's maiden Test, Kumble responded in positive.
Kumble said the team was not affected by the talks around DRS and pitches used in the two Test.
(REOPENS DEL 31)
Going back to the second Test, Kumble said the host nation showed character.
"I think Day 2 (of Bangalore Test) was fantastic. There was attrition. Only 190 runs were scored and six wickets were taken but the intensity and control with which our bowlers bowled, especially the pacers, showed character. That's what you want to see in a team -- a lot of character and pride in doing things and coming back and winning a Test match.
The spin legend patted his boys and said they responded well since he took over the reins.
"It's good we are playing so well consistently. From the West Indies series there have been many milestones. We have won all series. Virat Kohli has hit four double hundreds, (Ravichandran) Ashwin is the fastest to reach to 250 wickets.
Kumble showered praise on Umesh Yadav, saying the right-arm pacer always looks to pick up a five-wicket haul.
"The way Umesh has bowled, given breakthroughs, credit to him for the maturity he's shown. Every time he bowled he looked like getting a fifer. Happy for Ashwin but also glad how (Ravindra) Jadeja came up the rankings."
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