The Koreans scored early through Cheon Seul Ki (second minute) and Cheon Eun Bi Min (9th) and held on to those goals to deny the Indians victory.
India reduced the margin in the 41st minute through Ritu Rani, but failed to break through the Korean defence again.
India, who needed to win the Asia Cup to qualify for next year's World Cup, at The Hague, Netherlands, will play China in Friday’s bronze medal play-off.
Japan defeated China 4-1 in the other semi-final.
The Koreans, who scored 31 goals in their three group matches, went on the offensive from the start and shocked India by striking from two penalty-corners in the first ten minutes.
Cheon Seul Ki, a veteran of 71 international matches and one of the best drag-flickers in Asia, put them ahead in the second minute scoring from their first penalty-corner.
Seven minutes Cheon Eun Bi doubled the lead, making no mistake from another penalty-corner.
The Indians pressed hard but tight marking prevented them from making inroads into the Korean circle.
However, they were more cohesive in the second session and struck in the 41st minute when Ritu Tani scored from a penalty-corner.
Thereafter, India went all out in search of the equaliser but the Koreans gave nothing away.
Image: Action in the India-Korea semi-final on Thursday
Photograph: Hockey India