Smith's glance over to the dressing room for advice on whether to review a leg before wicket decision drew an explosive response from Kohli, who claimed it was third such time the Australian had sought assistance in the second test.
The allegation has been dismissed by the tourists, who collapsed to a 75-run defeat in Bengaluru after Smith's departure as India tied the series at 1-1.
Addressing a news conference on the eve of the third test on Wednesday, Kohli said he did not regret his attack on Smith, who admitted to having a spur of the moment "brain fade".
"I think about what I say. I don't regret anything that I've said," Kohli told reporters in Ranchi, which is hosting a test match for the first time.
"But at the same time, it's very important not to be stupid and go on with the same thing on a daily basis.
"We certainly don't want to sit and think about one issue all the time. We have two test matches to play and that's what we need to focus on."
The International Cricket Council (ICC) took a somewhat lenient view of the episode, opting against sanctions for any player, and both boards issued a joint-statement announcing a truce.
"It was a mature decision on everyone's part to move on from that," Kohli said. "We've seen instances in the past when it stretched too long and it just caused disharmony and there's no (other) outcome."
The episode has only enhanced Kohli's reputation as a feisty individual but India's batting mainstay remains unperturbed by how he is perceived in the media, especially in Australia.
"It does not matter to me honestly. I don't start a series saying 'focus on me, speak about me or write about me'. It's not in my control," the 28-year-old said.
"I'm not challenging anyone's opinion... I'm not going to hold a banner saying 'don't speak ill about me'. It's fine, it's all part of the whole journey.
"No one plays 15-16 years of international cricket without being criticised."
The controversy dominated Kohli's pre-match news conference to such an extent that the India captain appeared relieved when asked about what adjustments his batsmen had made to win in Bengaluru.
"Thank you for asking about cricket, finally," he said.
For his part, Smith said there was no lingering bitterness in his team over the incident.
"Not from my point of view. It's about moving on and concentrating on the test match here," he said.
"It's been a great series so far in the cricket that's been played. Hopefully cricket can be the winner out here in this test match.
"It's an exciting 1-1 halfway through the series. So we're all excited about this test match."
(Editing by John O'Brien)
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