Kumble resigned from his position as the head coach before the team left London for the West Indies.
India skipper Virat Kohli on Thursday took a dig at former national team coach Anil Kumble's comments in his resignation letter, asserting that sanctity of the dressing room has to be maintained.
Kumble, who put in his resignation on June 20, had offered a glimpse of his relationship with Kohli in his letter to the Board of Control for Cricket in India (BCCI), saying the partnership had become untenable.
"Obviously Anil bhai has expressed his views and he's taken the decision to step out and we will respect that decision. It's something that has happened right after the tournament. One thing for sure is that I've had 11 press conferences that have happened during the Champions Trophy. We have created a culture over the last 3-4 years that whatever happens in the change room, we've tried to maintain the sanctity of the change room throughout.
"That is what the whole team believes in. For us that is paramount. I've always respected that and we have continued to maintain that as well," Kohli told the media here on the eve of the first One-Day International (ODI) between India and West Indies.
Kohli had reportedly expressed his unhappiness with Kumble's coaching style in his conversation with BCCI officials.
Kumble's attitude towards discipline and his strict demeanour had reportedly not gone down well with several players.
The legendary leg-spinner's dressing down to the team following India's humiliating 180-run defeat to Pakistan in the Champions Trophy final in London on June 18 was also not received well by some players.
Kumble's tenure was supposed to end after the Champions Trophy but the Cricket Advisory Committee (CAC) of the BCCI extended it till the end of the upcoming West Indies tour.
However, Kumble resigned before the team left London for the West Indies.
"Like I said, for me what's most important is to maintain the sanctity of the dressing room and what happens in the change room is something that's very sacred and private to all of us, and something that I would not express in details in a public scenario.
"As I said, his point of view is out there and we respect that decision," Kohli said.
"It's his opinion, which I respect. I have total respect for him as a cricketer and what he has achieved (for the) nation. All the years that he has played... There's no taking away that aspect of him at all. And we all respect him totally."