This happened to me on a Air Transat flight to Toronto this Christmas: ds1 (4yo) got airsick due to turbulence (or maybe bad lunch???).
He managed to tell me that he needed the loo, where there was some queue. I asked to skip the line and fortunately people let us. When he was first in line he couldn't hold back and threw up in the small corridor leading up to the loo. One of the air crew saw me, said "yuck" and turned around (crew was preparing for the snack to be brought around the plane, so all gathering at the back of the plane). One of the other staff asked what was going on and then was told by the "yuck" stewardess that ds1 had just thrown up all over the place, and she said "we let the parents clean up". I was then given a total of 4 refreshing tissues (those wet ones that smell like lemon), and one small napkin, and told to get on with it. I said that with the supplies i was given i was hardly going to be able to do that.
Fortunately, after trying my best and feeling absolutely awful as poor ds1 was still standing there feeling misirable and saying "i am not a bad boy mummy???", another member of staff, from the 1st class section of the plane, was alerted by all the fuss and noise and came to see what was up. She spread some powder on top and gave me a stack of napkins to deal with the vomit and went to fetch a garbage bag.
I have no problem whatsoever cleaning after nmy own children, but really, they should have made slightly more effort to find me the supplies to do it with?
Should have complained with air transat. don't know why i didn't really. But we are sure never to fly with them again!