Arpinder, who had won a gold in the Asian Games in Jakarta, cleared 16.59m in the first of his three jumps to be in the four-man semifinals. He could only clear a 16.33m jump in his next attempt to miss out on the two-man final jump. Nonetheless, he collected a bronze.
The 25-year-old Arpinder was representing the Asia-Pacific team in the meet, held once every four years. He had jumped 16.77m in Jakarta and has a personal best of 17.17m which he recorded in 2014.
No Indian has ever won a medal in the Continental Cup which was known as the IAAF World Cup before 2010.
Reigning Olympic and world champion Christian Taylor of the United States easily took the gold with a jump of 17.59m, which is one metre more than the best effort of Arpinder.
The 28-year-old Taylor beat World University Games silver medallist Hugues Fabrice Zango of Burkina Faso, who cleared 17.02m, in the two-man final round.
Taylor, who was representing the Americas, has a personal best of 18.21m.
The IAAF Continental Cup is being competed in 37 events in men and women sections taken together with two top athletes from the four regions of Europe, Americas, Africa and Asia-Pacific taking part in each of them.
The format of four-man making it to the semifinals and then two competing in the final round was introduced this year with an aim to make the event more interesting.