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Eighteen wickets tumbled on an eventful third day of a low-scoring match with spinners from both sides wreaking havoc on a spiteful wicket.
Chasing 218 for win, South Africa were shot out for 109, with the Indian spinners claiming nine of the 10 second-innings wickets.
India spin S. Africa to defeat in first Test
Kohli insisted, however, that the track was anything but unplayable.
"There is no needs to unnecessarily hype up the wicket," the 27-year-old, in his first home series as test captain, told reporters.
"As (off-spinner Ravichandran) Ashwin said yesterday, we've never seen any hype around the wicket whenever we tour abroad. It should not be here as well."
No pitch worries for India, South Africa
Kohli admitted bowlers dominated the contest but said not a single dismissal was caused by any delivery which reared up awkwardly from a track sporting several cracks and offering big turn from day one.
"Throughout the game, not just the last innings, there were a lot of soft dismissals," the India captain said.
"I don't think there were any demons in the wicket. The ball didn't turn square at any stage. It was the batsman who had to apply more."
His counterpart Hashim Amla felt 218 was a stiff target for his team but blamed the Proteas batsmen for throwing away their wickets.
"150-160 would have been a pretty fair challenge on a deteriorating wicket like this. But at the same time, there were some soft dismissals during the chase," said Amla.
S. Africa's Elgar wrecks India in first Test
The match brought only three half-centuries and only one India managed to pass 200.
Stiaan van Zyl top-scored in South Africa's second innings with a gritty 36, while Amla's dismissal was bizarre as he offered no shot to a Ravindra Jadeja delivery and watched in dismay as it crashed on to his middle stump.
"I surprised myself (with the dismissal), it was a bit of brain-freeze really. I felt very unfortunate.
"I think we were into the game until we lost 4-5 wickets and put pressure on the lower guys. Stiaan particularly showed particularly that you can get runs if you can hang in there."
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