The coach's post was vacant since Shastri's 18-month tenure as the team director ended with India's semi-final exit at the World Twenty20 tournament on home soil earlier this year.
For the post, the Indian cricket board (BCCI) received 57 applications which were made available to an advisory panel that included ex-captains Sachin Tendulkar and Ganguly and former batsman VVS Laxman.
The panel met the final contenders, including Shastri who spoke via skype, before Kumble, a contemporary of the ex-cricketers on the panel, landed the job despite his lack of coaching experience.
Shastri told the Indian media that Ganguly's absence during his interview was disrespectful and he advised the former captain to be present at important meetings in the future.
Ganguly, one of the most successful Indian captains, said he had taken the BCCI's approval to attend a meeting of his state cricket association, of which he is the president.
"I just feel that the comments are very personal and if Ravi Shastri feels that I am responsible for him not being the coach of India, he's living in a fool's world," Ganguly told television reporters in Kolkata.
"It's a committee and there are people in the committee who are of more repute than I am and there are other people involved also who were consulted and spoken about. So that's disappointing."
Ganguly said the panel had agreed his request to resume the interview after completing the association's meeting.
"Once I came here to this meeting, I got a message from (BCCI secretary) Mr (Ajay) Shirke that the other two members are requesting if they could continue with Ravi, which I was fine with.
"I said 'fine, I know I have been stuck with this and you please go ahead and do it'. That happens everywhere in the world and that's the exact story."
Ganguly said Shastri should also have made the effort to be present in person during his interview.
"Since he's spoken about disrespect, and honestly I say this with anger, that he gave me a suggestion that in the future that I should be available for such meetings," Ganguly said.
"I have an advice for him also. When the coach of India is selected, and it's one of the most important jobs in cricket, he should be in front of the committee giving his presentation and not sit in Bangkok on holiday and make a presentation on camera, especially when someone, who is one of the greatest cricketers of India all time (Anil Kumble), spoke for two hours nearly."
(Reporting by Sudipto Ganguly; editing by Amlan Chakraborty)
