Jadeja and MS Dhoni put on 116 runs for the seventh wicket to fix the damage, but their wickets spelt the end for the pre-tournament favourites.
"So close, yet so far for India".
Boult and Henry shared five wickets while spinner Mitchell Santner claimed two in a tight display to snuff out India's hopes.
One such moment came after - Jadeja reached his half-century and performed his signature sword celebration to keep India's chances alive in the contest - opener Rohit Sharma gestured towards the southpaw from the dressing room. However, I think Virat Kohli was unlucky as it was a poor decision to give him out. Jadeja had speared the ball high but Williamson showed ice-cool nerves to hold on to the skier. "And had Dhoni dived, who knows, he wouldn't have got run-out and would have taken India across the finishing line", he added.
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Virat Kohli reacts to criticism after Indias World Cup exit
New Zealand will now play either Australia or England in the finals to be played on Sunday at Lord's. Eventually, it became a too tough a task to complete as India fell short by 18 runs.
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Kohli also quashed any knowledge of Dhoni potentially retiring, saying the veteran wicketkeeper-batsman has not spoken to him about his future plans. "Dhoni is an absolute legend".
"But whatever happens it's going to be a great occasion, and the Black Caps can go into that game with a lot of confidence behind them".
Kohli insisted the defeat, which came after India won seven of nine group games, will eventually be dissected to work out what went wrong. "However, he was unfortunate and couldn't take India to the finals".
His comments have been severely criticised by cricket fans from all over the world on the social media platform as the former Indian captain is respected by people for his contribution to the game of cricket.
"Only every four years do you get the opportunity to play in a World Cup, let alone make a final", added Williamson, as wives and girlfriends of the New Zealand squad, many clad in replica shirts, together with some of the players' children, mingled on the outfield at Old Trafford.