Pressure has mounted since India lost their World Cup semi-final against New Zealand, with former captains Gavaskar and Sourav Ganguly leading the onslaught.
India have brought in a host of younger players for their three Twenty20 internationals, three one-day matches and two Tests starting on Saturday.
Kohli, Rohit Sharma, Shikhar Dhawan, K.L. Rahul, Rishabh Pant and Ravindra Jadeja are the only players selected in all three formats for the tour, while rising stars Manish Pandey and Shreyas Iyer are in the limited-overs team.
“I´m opposed to too many players being moved around. I´m for stability, not a stop-start type of an environment,” Ganguly told The Print news website.
“We haven´t won a global tournament since the 2013 Champions Trophy.
“We have to find a way to move beyond the last-four stage. Look at what England did in the recent World Cup. Learning from 2015, they transformed themselves into world beaters.”
Ganguly said there had to be “clear” communications between the selectors, team management and players.
“We don´t need cameos only, we need match-winning innings or spells. Learn from Virat, Rohit (Sharma) and (Jasprit) Bumrah… Mohammed Shami too.”
Gavaskar launched his “lame ducks” attack because Kohli´s appointment as skipper for the West Indies did not go through the normal protocol.
He said the selection committee did not meet to reappoint Kohli as captain.
“That they selected the team for West Indies without first having a meeting to select the captain brings up the question of whether Virat Kohli is the captain of the team at his or the selection committee´s pleasure,” Gavaskar wrote in the Mid-Day newspaper.
“To the best of our knowledge his appointment was till the World Cup. After that, it was incumbent on the selectors to meet even if it was for five minutes for his reappointment.”
He added: “By bypassing the procedure, the message that goes out is that while the players like Kedar Jadhav, Dinesh Karthik get dropped after below expectations performance, the captain continues despite much below par expectations where the team did not even reach the final.”
Selectors´ chairman M.S.K. Prasad rejected the criticism, telling the Press Trust of India news agency that pundits´ jibes only make the selectors “stronger”.
Prasad, who played just six Tests and 17 ODI between 1998 and 2000, said selecting a side is specialised job and experience as a player alone does not guarantee success.
“If international experience is the case, then many ex-cricketers, who have played a lot of first-class matches can never ever dream to become India selectors,” said Prasad.
“We have utmost respect for the legendary cricketers,” he insisted.