According to information received here, the 17-year-old, who was India`s solitary participation at the World Cup Final, had a 4-2 lead at the end of the third set, but in a dramatic finish the Ranchi girl lost out 5-6 to miss the gold and emulate Dola Banerjee`s feat.
India have only one gold medal in one of World Cup Final leg courtesy Dola had won in Dubai, three years back.
Deepika, who has already secured an Olympic quota for London 2012, had a terrific run in the final held at the picturesque shores of the Bosphorus where East meets West as the Commonwealth Games double gold medalist beat promising 16-year-old Mexican Alejandra Valencia who won a bronze medal at the Ogden World Cup (Stage 3).
But the reigning World Junior champion had her best win when she ousted Beijing Olympic bronze medalist Berengere Schuh of France in the semis to set up a summit clash against World Cup Stage 3 gold medalist Cheng.
The Indo-Chinese duo had a spectacular start in the final, with both firing in 10-10 each to start the first set.
But in the third set of arrows, Cheng shot a 9 while Deepika got an 8 as the Indian trailed the first set 0-2 with scores of 28-29.
It was a dramatic ending in the second set that saw Deepika equalise 2-2 after the Chinese managed 6 with third arrow.
Cheng started with 10-9 and needed an 8 to win the set and lead 4-0 but she had a poor shot as Deepika was happy to take the two points at stake and tie the match at 2-2.
In the third set, the Indian took advantage of a 7 by Cheng to take a 4-2 lead.
The fourth set was reversed with Deepika shooting a 7 at her first arrow which became the turning point for the Indian as Cheng made a comeback to make it 4-4.
But there was more drama in store with Cheng opening the final set with a 6, compared to Deepika`s 9.
However, Deepika could not be consistent as she shot 8 and 9, compared to Cheng`s two perfect 10s for a stalemate at 26-26.
In the ensuing shoot-off, Cheng scored a good 9 close to the 10-ring as the 17-year old needed a perfect 10 to clinch the yellow metal.
The teenager gave in to pressure, finishing with an 8 to hand Cheng the gold medal.
But the biggest win for Deepika came in the semis where she stunned 2008 European champion Berengere with a 6-0 thrashing.
It was in fact a sweet revenge for Deepika who lost out to the Beijing Olympic team bronze medalist in the recently concluded World Cup Stage 4 in Shanghai.
Deepika overcame strong breezy condition for a solid 9-9-10 start and win the first set 2-0.
The Indian scored the only 10 of the match in the second set and together with two 8s, it was enough for Deepika to add two set points and lead 4-0.
The Frenchwoman seemed too much disturbed by the wind and scored two 7s in the third set to hand Deepika a superb victory.
In the quarters, Deepika was pitted against another 17-year-old Valencia, who won the cadet bronze medal at the Youth World Championships in Legnica.
Deepika had a confident start to win the match 6-4. The men`s title went to World No 1 archer, Brady Ellison of the US. He defeated Dia Xiaoxiang of China 6-2 in the final.
World`s 32 best archers, including 10 world champions, make the World Cup Final that is held after the four stages of the World Cup.
Deepika had her maiden World Final appearance last year in Edinburgh, but she returned empty-handed, while Jayanta Talukdar won a bronze medal.