Ravi Shastri has expressed his disappointment at missing out on the role of India head coach, suggesting he could have done little more during his stint as team director.
Former leg-spinner Kumble was appointed as India's new coach on Thursday, following a recruitment process that involved the input of a cricket advisory committee featuring Sachin Tendulkar, Sourav Ganguly and VVS Laxman.
Shastri had served as team director from August 2014 up until April of this year, leading his country to the summit of the ICC Test rankings for a brief period.
India also remained a leading force in limited-overs cricket under Shastri, albeit without making the finals of the two global events for which he was at the helm.
Asked if he was hurt to be overlooked, Shastri told the Indian Express: "I was very disappointed. [There was] disappointment because of the hard work the entire unit had put in in the last 18 months.
"To see where they were when the support staff and I took over and to where they reached in 18 months makes me feel proud. Number one in Test cricket, number one in T20, number two in ODI. You can't ask for more.
"Even I didn't expect such a transformation in 18 months with this young team. I feel really proud. I was honest, worked hard along with the support staff, and the players were fantastic.
"You look during those months with the BCCI [Board of Control for Cricket in India] being hammered in the court and media for various reasons, cricket was the shining light. People really took to watching the way the Indian team was playing."
Shastri, who revealed Ganguly was not present in his interview for the role of head coach, added: "I think Anil inherited a damn good team, a fantastic team in all formats and his job would be to take it forward.
"I am proud of the boys and I would miss their company because I will treasure the joy and enjoyment they gave me in those 18 months. I am always there for them. They know that."