Cook said batting was near impossible on the newly laid strip at the refurbished stadium in Ahmedabad.
The wicketkeeper-batsman was bought by RCB for his base price of Rs 20 lakh.
Kohli was heard complaining to the umpires on the fourth day of the match which India went on to lose by 227 runs.
The skipper also defended the decision to play rookie left-arm spinner Shahbaz Nadeem instead of a more experienced Kuldeep Yadav after India were outplayed by England in the opening Test.
The win also boosted England's chance of reaching the final of the inaugural World Test Championship in June on home soil.
Kohli, speaking online to the media ahead of the first Test against England, did not divulge the details of the "brief" conversation on the matter.
Does the widespread appreciation for the undemonstrative manner in which Rahane led the team Down Under signal a greater comfort among the followers of the game than the aggressive “in your face” style favoured by Kohli?
Warner also joked that Kohli is his daughter's favourite player, besides himself, and Australia limited overs captain Aaron Finch.
Left-arm spinner Axar Patel has also found a place in the 18-member squad for the first two Tests.
Bumrah, key to India's attack, sustained the strain during the drawn third Test in Sydney.