Pant had been seen as the successor to M.S. Dhoni, now established as one of the country's all-time greats, but pundits have turned on the 22-year-old in recent months.
Pant, already overtaken by Wriddhiman Saha in the Test team, has been criticised for throwing away his wicket as a batsman and some misses behind the stumps.
Kohli said that Pant has to work on his game but insisted that fans who call for Dhoni's return are "not respectful".
"We certainly believe in Rishabh's ability," said Kohli.
"It's the player's responsibility to do well, work hard," the captain added.
"But I think it's a collective responsibility of everyone around us as well to give that player some space to do that.
"If he misses a chance or something, people can't shout 'MS' in the stadium. It's not respectful because no player would like that to happen."
Despite the questions over wicketkeeping, Kohli insisted that India, who started a limited-over series against West Indies on Friday, are close to finding their best team for the Twenty20 World Cup next year in Australia.
India top the Test rankings and are number two in the 50-over format behind England but are just fifth in the T20 world standings.
But Kohli believes the ranking is not a true reflection of India's abilities.
"T20 is a format where you experiment a lot more things than ODI and Test cricket," so the "risk" is higher, said the captain
"As a team you want to give chances to youngsters. So you can't really pinpoint where we stand. Ranking is actually the reflection of the strongest eleven but we haven't really played the strongest eleven together for many games."
Kohli is now back with the squad after resting for the T20 against Bangladesh that India won 2-1.
Fast bowlers Mohammed Shami and Bhuvneshwar Kumar have also rejoined the T20 squad with spin bowling all-rounder Ravindra Jadeja.
"For us it's about figuring out who are the players that can make a transition into international cricket and this a good format to see them," said Kohli.
"Heading into the World Cup, rankings are going to be irrelevant because in T20 anyone can win on the day. I think our combination is getting stronger and stronger.
"We will probably be playing as close to the eleven that we want in the World Cup as possible for the remainder of the T20 games we have leading into the World Cup."