Read: Seven-star Herath spins Sri Lanka to dramatic win against India
India dominated most of the match after dismissing Sri Lanka for 183 on the first day and taking a first-innings lead of 192 but Dinesh Chandimal's swashbuckling unbeaten 162 allowed the hosts to stage a fight back.
The experienced Rangana Herath picked up seven wickets while young off-spinner Tharindu Kaushal took three to bundle out India for 112 and power Sri Lanka to a spectacular comeback win by 63 runs.
"We did not counter what was being thrown at us. The need of the hour was to take calculated risk when you are chasing a small total," Kohli told reporters.
"The intent has to be there which I think was lacking. It's something we need to improve on.
"It was a case of us not playing fearless cricket and not going out there and being positive. We have been let down by our batting today. There are no excuses."
The hosts, who lost their last test series at home to Pakistan, put immense pressure on India with tight bowling and smart catches in the first session on Saturday.
The batsmen failed to find scoring opportunities, with first-innings centurion Shikhar Dhawan taking 36 balls to score his first run.
That came from a streaky four with the ball narrowly missing the leg stump after taking an edge.
The lack of runs allowed Sri Lanka captain Angelo Mathews to surround the batsmen with close fielders, hastening India's capitulation.
"We have had batting collapses in the past as well where we have lost wickets in bunches," Kohli added.
"Every time if you sit down and analyse it's been because we have ended up being too tentative.
“Today was a classic example of guys not backing themselves enough to express their ability out there. You have to do something to disrupt a bowler's length."
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