In addition to the factual and technical notes by Johnny Bones, let's also consider what an award is in the first place.
In many cases, an award is presented and distributed by an agency standing apart from the groups qualified for being awarded. In some cases, like the AMPAS the committee is supposedly a collection of professionals within the organization but really, who knows for sure? Who gets nominated and why is a matter of contention, but it ultimately follows a set of rules which are not important to list here. Some believe the probability of being nominated is offset by the amount of money one budgets for campaigning for such things.
Whether or not it's all true is not as important as whether or not it's all just a bunch of useless noise to people who are more interested in the work they produce. Some film makers and writers do it because they love doing it, must do it, or their work speaks for itself and their futures are not contingent on the number of accolades they have collected over the years.
Psychologically speaking, it is possible that Woody Allen just didn't care to pander to a ritual that makes no sense to him. I agree, as I could not care less if I was awarded anything. Nobel, Congressional Medal of Honor, Oscar. They all mean absolutely nothing to me and I am unknown in a field where having such awards may actually benefit my so called career. I wouldn't even respond if I was nominated. Even though there are numerous quotes from Woody Allen on the subject, the foundation for his disinterest is most likely in a confidence in his own work that never needed affirmation from anyone else. Like a comedian who makes the whole room laugh - that alone is the affirmation they needed, whether or not a panel of goof balls decided to give them a small statue to recognize this.
Not to be an A-Hole, but there's also the notion of who else holds this award. How do we know he doesn't just despise someone or many who have been awarded? Maybe he thinks of himself apart, or above some of the industry standards defined by who has been awarded in the past. To him, winning an oscar might be akin to "polishing a turd" ... Like if Adolf Hitler was awarded a Nobel prize. Every other holder pretty much throws that award in the trash at that point.
Any official notation on the subject is pretty easily found through Google searching. I added this blurb just to give a personal note. I work for an agency that just won the top award at some thing I don't care about. But my not caring about it is why I can relate to Woody Allen on this subject. I simply cannot find it in me to concern myself with what a panel of people have decided is the best. It seems so self serving, and reciprocal. What a silly little game.