The last round went well for both Indian men and women as they scored fine victories over Norway and Azerbaijan respectively.
However, the men lost the penultimate round encounter against Russia by 1.5-2.5 that cost them a medal.
The women were quite lucky to win the penultimate round encounter against Vietnam as both D Harika and Tania Sachdev fought back from nearly lost positions to save the day for their side.
Harika took a rest against Azerbaijan but that did not deter the Indian eves from winning comprehensively for a fourth place finish.
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China won the championship in the open section with 16 points while Russia finished second on 15 points. Poland snatched the bronze on 12 points, a point clear of the Indian men.
The Indian men had also finished fourth in the last Chess Olympiad held in Azerbaijan last year.
The Chinese were clinical in the last round as they scored 2.5-1.5 victory over Poland, thanks to a fine victory by Li Chao on the fourth board. The Russians were ferocious as they handed out a 4-0 defeat to the United States.
On the other boards Vidit Gujarathi played out a draw against Aryan Tari while Krishnan Sasikiran signed peace with Lars Oskar Hauge.
In the women's section, the Russians proved their supremacy over Ukraine defeating their neighbours 3-1.
It was a big heartbreak for Ukrainian ladies as they were in joint lead going in to the last round and yet could not win the medal as the margin of defeat upset their equation.
It was a three-way tie for the third spot with Georgia, India and Ukraine and as the tie was resolved the Georgians came out on third spot, thanks to 1.5 game points more than India. Ukraine finished fifth.
Results after Round 9 open: Norway (2) lost to India (11) 1-3 (Aryan Tari drew with Vidit Gujarathi; B Adhiban beat Johan Soloman; Frode Elsness lost to Murali Karthikeyan; Krishnan Sasikiran drew with Lars Oskar Hauge); Ukraine (6) beat Egypt (0) 2.5-1.5; Turkey (10) lost to Belarus (8); Russia (15) beat USA (8) 4-0; China (16) beat Poland (12) 2.5 -1.5.