I'm looking for a short story, obviously an allegory for the postwar refugee problem,
The story is "DP!" by Jack Vance, first published in Avon Science Fiction and Fantasy Reader, April 1953, available at the Internet Archive.. The term "DP", short for "displaced person", was commonly used at the time to refer to the postwar refugees.
in which the effects of aerial bombing cause a previously unknown race of underground–dwelling humanoids to be forced to the surface after World War Two,
The humanoids are called "troglodytes" or "trogs". The reason for their emergence seems to be unrelated to aerial bombing:
"In our conversations with the trogs we have endeavored to ascertain the cause of the migration. Not one of the trogs makes himself completely clear on the subject, but we have been given to understand that the great caves which the race inhabited have been stricken by a volcanic convulsion and are being gradually filled with lava. If this be the case the trogs are soon to become literally 'displaced persons.'
where they are helpless and destitute.
"Sooner or later our organization will break down; more trogs will come up than it is within our power to feed. Organization already has failed to some extent. All the trogs are getting at least one meal a day, but not enough clothes, not enough shelter is being provided. Every day hundreds die from sunburn. I understand that the Old-Clothes-for-Trogs drive has nowhere hit its quota; I find it hard to comprehend. Is there no feeling of concern or sympathy for these people merely because they do not look like so many chorus boys and screen starlets?"
Humanity squabbles ineffectually about how to deal with them
New York, June 4: By a 35 to 20 vote—exactly reversing its first tally on the measure—the U. N. Assembly yesterday accepted the motion of Mexico's Hernandez to set up a committee for the purpose of recommending a percentage-wise distribution of trogs among member states.
Tabulation of voting on the measure found the Soviet bloc lined up with the United States and the British Commonwealth in opposition to the measure—presumably the countries which would be awarded the largest numbers of the trogs.
and they die off.
"I don't know why I should be sitting here writing this, because—since there are no more trogs—there is no more trog story. But I am seized by an irresistable urge to 'tell-off' a rotten, inhumane world . . ."