England's Jos Buttler made 59 and Rahul Tripathi hit the winning runs with a six from the penultimate ball as Rajasthan Royals made 164/3 to secure their first win of the season by seven wickets.
While India top the Test rankings and Kohli is the leading batsman, he looks increasingly frustrated at his side's Indian Premier League performances.
He has never won the IPL title and Bangalore are now rock bottom in the eight-team league -- the only outfit without a win.
Kohli bemoaned Bangalore's failure to set a more challenging target against Rajasthan as well as dropped catches in the field.
"If we make that many mistakes, then you are going to fall on the losing side," said Kohli after the game. "In a tournament like the IPL, when you have no momentum then these things can happen.
"The team hasn't got off to a good start and these things look really bad but we have to keep believing that we can turn things around."
Kohli acknowledged that the injury-hit team may need changes as he said: "We will sit down and talk to see how we can balance our team. Hopefully we will get fresh guys in and they can give a match-winning performance."
But Bangalore now need a radical improvement to reach the playoffs, and questions are already being asked about Kohli's leadership and the failure to get an IPL title in what is now the tournament's 12th season.
Former India opener Gautam Gambhir said the India batting great was "very lucky" to be retained as captain by his franchise.
Former England captain Michael Vaughan ridiculed Bangalore's tactics.
"They look in shambles, the strategy they had pre-tournament has all been ripped. They are just picking tactics out of the hat as they go along," Vaughan told the Cricbuzz website.
Vaughan said IPL front-runners like reigning champions Chennai Super Kings, Sunrisers Hyderabad and Kolkata Knight Riders stick to winning strategies.
Bangalore have ended the last two editions in sixth and eighth spot despite having top players like Kohli, South African AB de Villiers and the big-hitting Chris Gayle.
The side were undone by an umpiring error last week when Mumbai Indians paceman Lasith Malinga got away with a no-ball on the last delivery of the match with Bangalore needing six to tie.
The giant screen on the ground later showed Malinga overstepping the line and a fuming Kohli lashed out at the "ridiculous call" that cost his team a chance of victory.
But on Sunday they went down by 118 runs to Sunrisers Hyderabad in what Kohli called one of Bangalore's "worst losses ever".
"We were outplayed in all departments by a quality side," the Indian captain said after watching Jonny Bairstow hit 114 off 56 balls to guide Hyderabad to a stunning win.