A vociferous lbw shout was shot down when footage confirmed Shaun Marsh edged the ball onto his pads. Ashwin was convinced Matthew Wade gloved a ball before it ballooned off his chest, but replays showed a clear gap between ball and glove.
Marsh, who scored 66, would have been dismissed for 14 had Kohli opted to review an earlier caught-behind shout.
Kohli have lodged over 40 reviews since the start of the England series, when India's stern resistance to adopt DRS ended. Some 34 have been struck down.
"We have been working on it, at times there were close calls and we didn't get it right," India's Cheteshwar Pujara said.
"There was one instance where Shaun Marsh was out and we didn't take the review, we were not sure and we got it wrong.
"We are working on it and can get better at DRS."
Injured opener Murali Vijay shared similar words last week, but Kumble was fiercely defensive when asked about India's DRS problems in Pune.
"I don't think we messed it up," Kumble quipped, prior to the start of the second Test.
"You can always have hindsight ... but those calls were really close, so I don't see a reason why we need to worry too much about that."
Marsh was given out on 44 but successfully reviewed his lbw dismissal, while Steve Smith used a referral to help Nathan Lyon bag the sixth of his eight wickets on day one in Bangalore.