The English pairing had seen the men's team reach the last four of the competition earlier in the day, but they were unable to replicate that achievement as they were beaten in a tightly-contested encounter.
Grimson and Palmer got off to a good start with victory in the opening set, saving match point at one stage before going on take it 23-21.
It looked as though England were on course for a semi-final spot when they led 18-14 in the second set too, but the Vanuatu duo of Miller Pata and Linline Matauatu then won seven of the next eight points to take it 21-19.
That took the match to a deciding set - first to 15 rather than the conventional 21 - and in the end it was a number of faults which cost England as Vanuatu sealed the 15-12 win.
Vanuatu, who are now guaranteed a shot at at least a bronze medal, will next meet either Rwanda or hosts Australia in the semi-finals.