Kohli, who was put down on 21 by Rovman Powell off the bowling of Kartik Tyagi, went on to produce a match-winning unbeaten 105 from 60 balls as RCB chased down a target of 193 to move to the top of the standings.
The veteran batter anchored the innings superbly and shared a vital 92-run partnership for the second wicket with Devdutt Padikkal, who added 39 runs during the successful chase.
Despite the defeat, Nayar believed Kolkata had enough runs on the board but said the game slipped away because of "small mistakes", with the dropped chance proving decisive.
Nayar also acknowledged KKR's dependence on experienced spin duo Sunil Narine and Varun Chakravarthy, who have played a major role in the team's bowling performances this season.
"When you drop Virat Kohli, especially in a chase, it becomes very difficult," Nayar said at the post-match press conference.
"As I said earlier, the score was fine on this pitch. There are a lot of things that could have been better. Virat's catch was a very tough one. The Angkrish catch, you would expect him to take.
"At the end of the day, cricket works like that. If we had another 10-15 runs, maybe the game changes. If those catches are taken, maybe the game changes."
Nayar also went on to praise Angkrish Raghuvanshi's knock of 71 from 46 deliveries.
"I was very impressed with the way he batted because the ball was really nipping around early on. Hazlewood and Bhuvi are world-class bowlers," Nayar added.
"At no point did he look uncomfortable. He looked like he belonged there."