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Speaking to the Guardian, Shastri said there was a "gang of people in India" who always wanted him to fail.
Just like Shastri, Key has been an acclaimed commentator for a long time and though he doesn't have a coaching degree, he tries to ease into a different role.
"I didn't have coaching badges [either]. Level one? Level two? f*** that," Shastri said. "And in a country like India, there is always jealousy or a gang of people willing you to fail. I had a thick skin, thicker than the leather of the Dukes ball you use. A real solid hide.
"And you need a bloody hide over here. Rob will develop this as he does the job because every day you are judged. And I am glad he has a lot of captaincy experience from his time at Kent, because communication with the players is absolutely paramount."
From his own experience of working with the Indian team, Shastri felt that national teams across the cricketing world function in a pretty similar fashion.
"Rob may have more work with the domestic game but, when it comes to the national team, it is very similar," Shastri said. "The most important thing is getting among the players and setting a tone from the outset: what you believe in, what you think of them and changing the mindset to compete and win.
"You have to be bullish and brutish in wanting to achieve that. For us, and now England, it was about setting the challenge of winning abroad, big time. I was very firm when it came to team culture: all the prima donnas and all that sh**, that had to go out of the window early."
Outlining the philosophy and team culture is important, according to Shastri, and that's what he had drilled into the India team when they beat Australia in two back-to-back away Test series.
"...It was also outlining how we want to play: to be aggressive and ruthless, to up the fitness levels, to get a group of fast bowlers to take 20 wickets overseas. And it was about attitude, especially when playing the Aussies. I told the boys if one single 'f** you' comes your way, give them three back: two in our language and one in theirs."
Shastri also said that Key needs to discuss England's issues with former Test captain Joe Root.
"Rob will have an adjustment period to understand the issues and will need to speak in detail with Joe Root for his experiences as Test captain. But in my 24 years [commentating], I did not miss a beat or a ball of Indian cricket," he said.
"And he [Key] will have covered a huge amount too. So you're not lagging behind by an inch, you're abreast of what a team requires but also what other teams are doing. You should be able to leapfrog over all those early issues and get into the nitty gritty straight away." Shastri felt that Ben Stokes would be the ideal choice to take the England team forward.
"The adrenaline of captaincy - not that he needs it - could fire Stokes up to be something even more than the incredible player he is now. The important relationship is with the captain - the moment there is friction, things go downhill.
"But they will be fine because the England I saw last year, they have enough talent and skill to compete. There's no doubt about that in my mind. It's all about their mindset."