For centuries there has been the expulsion and persecution of people in the world, particularly the Jews who were expelled from many European countries long, long before World War II. Perhaps this fact contributed to the avoidance of recognition at first to the plight of the Jews and Catholics and other religious sects.
There are some individuals and groups who, to this day, deny that the Holocaust ever occurred. See http://en.wikipedia.org/wiki/Holocaust_denial for an exploration of the alternate interpretation of history advanced by these persons.
My point in bringing them into the discussion is to point out that people can choose to rationalize anything through selective use of facts and ideas placed in carefully constructed contexts with omissions of other facts as necessary.
I think what is more interesting about the Holocaust is how the world responded later on rather than its incredulous, disbelieving response to begin with. The way in which it sought to come to terms with it and the horror of the reality of what happened sunk in gradually and we can see the creation of Israel in part as a response to the feelings of immense sadness and guilt about the sufferings of the Jews.
As the other posts mentioned, the world was very slow when it came to responding. Partially this was due to the sheer shock value. No one really thought that the Germans would act in this fashion. Many Jews did not even think it would go this far. When the war broke out, there was little that the world could do. They just needed to win the war to free people from the oppressive and evil Nazi regime.
Despite the fact that the Allied Powers spoke out publicly against the "systematic extermination" of the Jews as early as 1942, they refused to take actions that may have saved lives. The United States refused to alter its immigration quotas to accomodate Jews who were fleeing Europe, sometimes with tragic consequences. FDR refused to divert American bombers to destroy rail lines to Auschwitz late in the war.
The world did not really respond to the Holocaust in any particular way when it was first found out. The world was in the middle of WWII and could not really do anything about the Holocaust at that point. After the war, the Allies prosecuted a number of Nazis for war crimes connected to the Holocaust.