India lost the match by 48 runs after giving a real shot to the 364-run target here and Kohli said he is proud of the approach.
"The chat I was having with guys in the middle was belief. If you believe in a stroke, go for it, I told them. Rohit (Sharma) was sweeping and missing, but I kept backing him. That's how we looked at the game and that's why we came so close to the target. If at any point we had played for a draw we would have lost by 150 runs to be honest," Kohli said in the post-match presentation.
At the Adelaide Oval, despite Kohli's career-best score of 141 runs, the visitors fell short of the target and were bowled out for 315 runs. They now trail the four-match series 1-0.
"Australia were far better than us in taking chances and grabbing opportunities. They deserved to win today," said Kohli.
"When Murali Vijay and I were batting in the middle, it looked like we had the upper hand. But at no point did I think that we have to pull out of the chase. I always believed that we could do it and backed myself throughout.
"There is enough reason to regret about things. But at the same we have to look at the positives. I look at every opportunity to do as something special for the team and if we were able to pull it off today, it would have been one of the most special moments of my life. But despite the loss I am proud of the way the boys played," he added.
Kohli became the second Indian batsman after Vijay Hazare to score two hundreds (116 and 148 in 1947-48) in a Test at Adelaide.
Among Indian batsmen, he became the fourth after Hazare, Sunil Gavaskar (thrice) and Rahul Dravid (twice) to achieve this feat.