Kohli was batting when Smith was sent to field on the boundary at one stage of India's innings. Spectators near Smith started chanting, "Cheater!" repeatedly but Kohli, in the middle, gestured to the India insignia on his helmet, pointed at Smith and clapped in an effort to quiet the crowd.
"Just because there's so many Indian fans here, I just didn't want them to set a bad example, to be honest, because he didn't do anything to be booed in my opinion," Kohli said. "He's just playing cricket. He was just standing there, and I felt bad because if I was in a position where something had happened with me and I had apologised, I accepted it and I came back and still I would get booed, I wouldn't like it, either.
"So I just felt for him, and I told him, I'm sorry on behalf of the crowd because I've seen that happen in a few earlier games, as well, and in my opinion that's not acceptable."
WATCH on Hotstar (India only) - Kohli detests crowd booing Smith
Smith and David Warner have been booed and heckled repeatedly on the field since their return to the Australian team following their one-year bans over the ball-tampering incident at Newlands. But while Kohli has had various run-ins with Smith - most memorably when he suggested Smith had deliberately sought guidance from the dressing room while deciding whether to review a decision during Australia's Test tour of India in 2017 - he said he felt for Smith in his current circumstance.
"Look, I think what's happened has happened like long back, the guy is back, he's trying to play well for his side," Kohli said. "Even in the IPL I saw him, it's not good to see someone down like that, to be honest. We've had issues in the past. We've had a few arguments on the field. But you don't want to see a guy feeling that heat every time he goes out to play.
"What's happened has happened. Everyone has known that. He's come back. He's worked hard. He's playing well for his side now."
Glenn Maxwell became aware of Kohli's gesture after the match and said he was not surprised with the aggressive Kohli on the field being different to the person they know away from the heat of the battle.
"It's nice to hear that, I'm not surprised by it because we do get along as individuals really well with him off the field," Maxwell said. "What happens on the field, that's for everyone else to write about but all we want to do is play our cricket hard. That's what he does, gets in the opposition's face which is great, but off the field I'm not surprised by that all."
Melinda Farrell is a presenter with ESPNcricinfo