The series was kept level at 1-1 after a draw in the third Test at Ranchi.
Kohli has yet to score more than 15 runs in the four winnings that he has played so far.
Kohli believes Australia crossed the line in the second Test in Bengaluru.
India's 19 Test match unbeaten run came to an end in Pune.
A total of 351 cricketers will be available to purchase at next Monday's auction in Bengaluru.
Tourists lost eight wickets for just eight runs chasing target of 203.
Joe Root controversially dismissed in the final over.
Eoin Morgan's men will attempt to build on their ODI victory over India last week.
Tourists successfully defend 321 in entertaining third ODI clash at Eden Gardens.
India clinch unassailable 2-0 series lead with 15-run win in Cuttack.
India were reduced to 63-4 but the captain led them back to take win.
Eoin Morgan and Jos Buttler both produce golden ducks as the tourists slump to heavy warm-up defeat.
35-year-old resigned as his country's ODI and T20 captain last week.
The 35-year-old gives up the ODI and T20 armband after 11 years.
The previous record by an opener was held by Surrey's Bobby Abel, who scored 357 not out against Somerset at The Oval in 1899.
Kohli was the leading run-scorer in the recently concluded Test series against England.
Without world-class spinners, winning in sub-continent conditions is going to be hard, the England Test skipper said.
Cook will return home and hold talks with director of cricket Andrew Strauss over role.
Tourists experience another woeful batting collapse to lose the fifth Test by an innings and 75 runs.
India and England are currently in action in the fifth and final Test match at Chennai.
Morgan has been named interim captain of Sydney Thunders in Shane Watson's absence.
However, India openers KL Rahul and Parthiv Patel mount an impressive response on day two of the fifth Test.