Sheikh came up with a career-best performance, shooting 121 in the qualifying and even getting the better of former world champion and world number 8 Jesper Hensen of Denmark in a shoot-off, but could not create the same magic in the final.
This was Sheikh's first ever World Cup final in seven years of skeet shooting and comes on the back of another final appearance in the recently held Asian Shotgun Championships in Abu Dhabi, where he had finished fifth.
Sheikh finished sixth with a total of 16 out of 20 shots, having missed a few early birds at the Dr Karni Singh Shooting Range.
Italy's Riccardo Filippelli (57) beat compatriot and reigning Olympic champion Gabriele Rossetti (53) for the gold medal in the final. Australia's Paul Adams (45) won the bronze medal.
"It was a good experience. I felt good but I missed a few shots. There is scope for improvement," said Sheikh.