Englishman Bairstow struck 114 from just 56 balls while Warner carried his bat for a 55-ball 100 in a record 185-run first-wicket partnership to post a mammoth 231 for two, a total which the visitors defended without any fuss.
This was RCB's third loss on the trot in the tournament.
"One of our worst losses ever. Literally nothing I can explain. Nothing went right for us from ball one until our last wicket fell in the second innings. We were outplayed in all departments by a quality side. They showed that they are a champion side - they were finalists last time and beat us in the final (in 2016)," a dejected Kohli said after the match.
Kohli credited Bairstow and Warner for taking the game away from his side with their explosive opening partnership.
"Credit to them (Warner and Bairstow). We could have tried a few different things, like taking pace off the ball. But once those guys got in, they just kept going. You need a few things to go your way, and a few catches fell in between fielders. They were world class today and they deserve to be on the winning side," he said.
Kohli said with a big total to chase, he thought of opening the batting but later decided against the option to give balance to their fragile middle-order.
"We thought about that initially as well (opening the batting). I have done well opening the batting but myself at number 3 brings that balance in the side, given that I can bat with AB (de Villiers) and put the opposition under pressure. We just need our players to put up a better challenge up front. There are still 11 games to go," he said.
"The pitch will be nice in Jaipur against the Royals. We need to bring our A-game, like we did against Mumbai and play with that kind of intensity. If we go through the motions, we need to do the regular basic stuff, and get results our way and start winning games in the tournament. The next game should be that game for us," Kohli said.
"It shows how good a spinner he is (Nabi). He was spot on from the first ball. It was a good batting track in the second innings but our bowling was brilliant," he said.