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Shimron Hetmyer hit a career-best 139 to lead West Indies to an eight-wicket win but the match saw controversy during India's innings.
In the 48th over, Roston Chase hit the stumps at the bowler's end where Jadeja was running and South African umpire Shaun George ruled not out.
But replays suggested Jadeja was short of his crease, prompting the on-field official to refer it to the third umpire who then gave it out, as an angry Kohli shook his head in disapproval in the dressing room.
"The thought is simple, the fielder asked 'how is that' and the umpire said 'not out'. The dismissal ends there," Kohli said after his team's loss.
"The people sitting on the TV outside cannot tell the fielders to then tell the umpire to review it again. I've never seen that happen in cricket.
"I don't know where the rules are, where the line is drawn. I think the referee and the umpires have to take that up, see that incident again. And figure out what needs to be done in cricket."
Jadeja made a quickfire 21 in his 56-run sixth-wicket stand with Kedar Jadhav, who made 40, as India went to score 287 for eight after being put into bat first.
West Indies skipper Kieron Pollard said no matter what happened but "the right decision was made".
"For me at the end of the day, the right decision was made, which is important," said Pollard.
"We appealed and the umpire didn't take it at that time, but eventually the right decision was made."
The second ODI is on Wednesday in Visakhapatnam.
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