The Indians, who are virtually assured of a place in the game's showpiece event to be held at The Hague, Netherlands, needed to win the eight-nation tournament to secure a direct entry in the World Cup.
Korea's fourth title win means Malaysia are certain to return to the World Cup after a gap of 12 years.
The Indians will now have to wait till the conclusion of the Oceania Cup in November, which either Australia and New Zealand is expected to win, for the official confirmation of their participation from the FIH.
The Koreans scored through Jang Jong Hyun (28th minute), You Hyo Sik (29th), Nam Hyun Woo (57th) and Kang Moon Kweon (68th). For India, Rupinderpal Singh (48th), Nikkin Thimmaiah (57th) and Mandeep Singh (64th) were the goal-getters.
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It was a case of near yet so far for the Indians who did a tremendous job in the second half, after going into the breather trailing by two goals.
But the Indians eventually fell short as Korea eked out a hard-fought win and also got their revenge over the Sardar Singh-led side against whom they lost 0-2 in the pool stage.
It was a fitting contest between the two top teams of the Asia as both India and Korea matched each other stick to stick.
The Indians started the match on a bright note and dominated the early share of exchanges, India made some good moves from the right flank but the forwards fizzled after entering the opposition circle.
Korea's game was all about putting the Indian defence under pressure through counter-attacks.