Many people have been discussing why the religious world (especially UO) doesn't observe Yom Hashoa, and why the religious world didn't make it's own day. I believe that there are 2 main reasons:
1. The Yom Hashoa ceremonies, are just that, ceremonies. As RYBS said (see Nefesh Harav pp. 94-95) Judaism does not believe in ceremonies. Whatever we do needs to be a kiyum of some din. To stand silent for 2 minutes is a ceremony taken from the non-Jews and has no kiyum in din. The Jewish response to tragedy is fasting, mourning, learning for the person etc., not ceremonies.
2. The Chazon Ish writes (Igros Chazon Ish letter 97) that to be קובע תענית is like to make תקנה דרבנן. Our generation is not on that level to do such a thing. And therefore he says we should not make any new day of memorial. We are not at the proper level to make such a תקנה. In other words, the proper response would be to קובע תענית, however we are not at the level to make such a תקנה. When chazal made dinim d'rabbanan they did it with soem aspect of ruach hakodesh which we lack.