Hi there! I completely understand your frustration, but I would also like to let you know about all your options.
Pigeons can be a nuisance, but finding dead birds at your favorite park isn't the most ideal situation.
I actually work for a company called Bird Barrier that is the leading manufacturer in humane bird control. Please take a look at our site http://www.birdbarrier.com/ to avoid this in the future. Hope this helps!