Exploiting their home advantage, India beat South Africa inside three days both in Mohali and Nagpur, while also dominating the rained-out second test in Bangalore.
This was South Africa's first away test series defeat in nine years and Kohli suggested there would be no respite for the visitors, currently the top-ranked test team.
"If you talk about mindset, we want to be ruthless," Kohli told reporters ahead of his first match as test captain at his home ground.
"We are not satisfied with two-nil. If we have a chance to go three-nil up, we'd try and go three-nil up and give our 100 percent."
The 27-year-old said the team would field the strongest combination even if the outcome would not alter the fate of the series.
"We are not going to field someone just because we are 2-0 up. At this stage, there is not much room for experiments," Kohli said.
Pitches used for the series have taken some sheen off India's achievement, with the Nagpur surface rated as "poor" by the match referee, while South Africa captain Hashim Amla called it the "toughest" track he has faced.
Kohli have steadfastly defended the tracks and the Indian captain once again resented the talk around the pitches, which he claimed "defied logic".
"We are criticised for our game and techniques when we don't play well. When the visitors don't play well, it's always the wicket. There is no sense to it," Kohli said.
"We are certainly proud of the way we have played in the series and we've won the two games in the series.
"We have nothing to run away from, no regrets, no hesitations about it. We are pretty happy as a team to go 2-0 up in the series."
Kohli was visibly annoyed when asked if he thought the test at Ferozeshah Kotla would go beyond three days.
"We are very confident. We have no issues in the team, regarding our confidence, ability or fitness," he said.
"Whether the match lasts three days, four days or five days, our aim would be to win it."
(Editing by Sudipto Ganguly)
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