Kumble, a spinner par excellence and a former India captain, tendered his resignation as chief coach after the ICC Champions Trophy due to "untenable" differences with skipper Virat Kohli.
On the eve of the second ODI against the West Indies here, questions related to the Kumble episode were directed at Bangar.
"We are professionals and such things are part and parcel of any organisation where changes happen. The support staff and the players have shown a lot of professionalism in compartmentalising the issues and so far we have coped up really well," said Bangar.
"Everyone's contributed towards it and as I said earlier, when you part ways it's never easy. You need to accept that at times such things are going to happen, have happened in the past. But what is of paramount importance is that Indian cricket should keep moving forward and the performances of the team shouldn't really be affected in any manner."
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Without a head coach, who also used to double up as the team's bowling coach, Bangar has his work cut out.
"Yes, Anil was doubling up. There were a lot of positive results under him. We all know that the team enjoyed a lot of success. The void, there is definitely a bit of lacuna but the experience that this team possesses - when you have a Mahendra Singh Dhoni, a Yuvraj Singh and Virat Kohli, who've played close to 700 international games, they're doing a lot of work behind the scenes, they are guiding the players."
Asked what defines the captain-coach relationship, Bangar stressed on trust.
"It's not only the coach and the captain, it's also the relationship and trust between the coach and all the players. Basically, it's a work in progress that requires a lot of time to earn the trust of the players.
"Once you do that, the job and the responsibilities of the coach become that much more easy. That is something that I've learnt to work (with)."
"It all boils down to the fitness part. If you're fit and capable of delivering. You saw in the match against Pakistan, how the experience came to the fore - In the last eight overs we scored 108 runs and that wouldn't have been possible without the contribution of Yuvraj Singh.
"Even when we were four down at Cuttack, it was the experience of Yuvraj Singh and MS Dhoni, who got two big hundreds and put us on a score of 360.
"They have done these things in the last four or five months and if they manage to keep themselves fit, motivated - and I can definitely vouch that they are very motivated to play - you can only stand to benefit from their continued presence in the team," Bangar concluded.