Gangjee had moved to tied fourth after two birdies in the first seven holes on the second day but slipped out of contention after a double bogey in the back-nine left him with a card of even-par 72.
All other Indians, including Anirban Lahiri, and Asian stars likes Liang Wen-Chong and Mardan Mamat also missed out.
Gangjee dropped down to tied 15th, despite being just two shots behind last qualifier, while SSP Chowrasia played a decent second round of 70 but his first round of 76 proved too costly.
Anirban Lahiri and Himmat Rai pulled out.
More From This Section
Meanwhile Japan's Hiroshi Iwata, who held the overnight lead, topped the 36-hole qualifying event when he signed off with a 71 for a two-day total of five-under 139 at the Amata Spring Country Club.
China's Wu Ashun will savour the prospect of making his second appearance at The Open Championship after he successfully earned one of the four tickets with a second round four-under 68.
Chinese Taipei amateur Pan Cheng-tsung will also get the chance to tee off against the world's best players after he posted identical 70s over two rounds to finish tied-second with Wu.