He, however, did not offer what led to Kumble's resignation coach on Tuesday, three days before the start of the limited-overs series in the West Indies.
"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," said Kohli on the eve of the first ODI of the five-match series against West Indies.
"It's [Kumble's resignation] something that has happened right after the [Champions Trophy] tournament. One thing for sure is that I have had 11 press conferences that have happened during the Champions Trophy. We have created a culture over the last three-four 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," he added.
The 28-year-old did not offer anything more on the issue, saying the "sanctity of the dressing room" had to be maintained.
"Like I said, for me what's most important is to maintain the sanctity of the change 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 (Kumble) point of view is out there and we respect that decision," he added.
Earlier, Kumble on Tuesday informed that Kohli had reservations about his work 'style' and his extension as the head coach, which prompted him to resign.
In a strongly worded letter, Kumble took to Twitter to reveal the reason behind his surprising decision.
Thank you! pic.twitter.com/eF5qVzdBRj— Anil Kumble (@anilkumble1074) June 20, 2017
Kumble said that although the BCCI had, several times, attempted to resolve the misunderstandings between him and the captain, it was apparent that the partnership was untenable, and therefore, he had decided to move on.
The statement from Kumble confirmed the reports about Kohli's alleged spat with Kumble regarding differences of opinion on selection matters.
However, Kohli before India's opening encounter at the Champions Trophy against Pakistan, had rejected the reports of him having rift with the head coach, saying they were mere speculations which have been created by the people.
Kumble was appointed coach in June 2016 for a one-year term by the CAC and was instantly successful. Under him, India won Test series against West Indies, New Zealand, England, Bangladesh and Australia.
And he was being considered the front-runner for an extension till the 2019 World Cup, with Team India having won almost every series under him in the past one year.
It was reported that the three-member CAC, who are tasked to find the new coach for the Indian cricket team, was willing to retain the legendary leg-spinner for the post.
The BCCI has now deputed its general manager Dr M.V. Sridhar to supervise the team management for the West Indies tour. Meanwhile, Sanjay Bangar, and R Sridhar, will continue to remain the batting coach and the fielding coach, respectively.