Kohli was seen remonstrating with the umpires after a controversial dismissal.
The India captain will return to India after the first Test in Adelaide.
The Board of Control for Cricket in India on Wednesday came out in strong support of India captain Virat Kohli and requested the International Cricket Council to take note of Australian skipper Steve Smith's 'brain fade' in seeking dressing room's advice for a DRS referral in the second Test.
The tweet came after Anil Kumble's resignation from the post of India's Head Coach earlier in the day.
Kohli's deputy Ajinkya Rahane will lead India in the final three Tests.
Cricket icon Sachin Tendulkar joined a host of former greats in congratulating India's cricket team on the historic series triumph over Sri Lanka on Tuesday.
India's newly-appointed batting coach Vikram Rathour says the opening slot and performance of the middle-order in ODIs are his primary concerns as he prepares to begin his tenure with the series against South Africa.
'Virat suffered a neck sprain during an IPL match in Jaipur.'
Kohli, who was named man-of-the-match for the 2nd Test that India won against Sri Lanka in Nagpur on Monday, will play the third and final Test in New Delhi.