Waugh, one of the toughest and most successful captains of all time, said he was impressed by Kohli's action of asking the crowd to not boo Smith, who is continuing to cope the fans' ire after returning from a one-year ban for ball-tampering.
"Leadership reveals itself in many forms but I thought Virat Kohli's gesture in calming down the rough reception given to Steve Smith from the Indian spectators was a class act that calmed a volatile situation," Waugh, who led Australia to World Cup title in 1999, wrote for the ICC.
During the clash with India here on Sunday, which Australia lost by 36 runs, the Indian fans booed Smith and chanted "cheater, cheater" when the defending champions were fielding. Kohli urged them to calm down and instead cheer his batting.
"I just felt for him, and I told him, 'I'm sorry on behalf of the crowd because I have seen that happen in a few earlier games as well'. In my opinion, that's not acceptable," the Indian captain had said in the post-match press conference.
Waugh said India's 36-run victory in the high-pressure World Cup clash will provide them with enormous confidence as they move forward in this tournament.
"India against Australia was always going to be a highly charged encounter between two teams that have met on numerous occasions over the past 12 months. This rivalry has revealed no clear dominance by either," he wrote.
"India's batting display was both measured and calculated with their plan clear and well executed. Their plan is to lay a foundation by not losing wickets and they stuck to it."