As the propaganda minister, yes he would of been in control of spreading hatred for Jews, but it is hard to condemn that during wartime when spreading hatred and dehumanizing your enemies is standard practice. And it might not qualify as heinous enough to actually count as a crime against humanity.
Lets take a look at that. There is a disparity you are not acknowledging.
Soviet Union: Country with government at war with Germany, had army, navy, air force in massive quantities
Poland: Country with government at war with Germany, had army, navy, air force in meaningful quantities
France: Country with government at war with Germany, had army, navy, air force in significant quantities
United Kingdom: Country with government at war with Germany, had army, navy, air force in significant quantities
USA: Country with government at war with Germany, had army, navy, air force in significant quantities
Jews: Peaceful ethnic minority in Germany and other parts of Europe that often made important contributions to society.
Germany treatment of the prisoners of:
Russia: severe mistreatment, many died
Poland: severe mistreatment, many died
France: Relatively humane treatment
United Kingdom: Relatively humane treatment
USA: Relatively humane treatment
Jews: Germany used modern bureaucratic methods and tools of industry in an attempt to exterminate all Jews in German occupied territory.
On what reasonable ground could Jews be targeted for even worse treatment than the Russians? They were productive members of German society, not an invading foreign nation. They were targeted for death based purely on ethnic/religious hatred.
It is easy to condemn Germany, the Nazis, and Goebels for the propaganda in service of genocide against the Jews, and the genocide itself, not to mention the waging of wars of aggression by Germany.
If that gruel is too thin for you, fear not. Goebbels had a more direct hand in the Holocaust as well.
Making Berlin 'Judenfrei'. The decimation of Berlin's jewish population by railway deportations.
Now, more than elsewhere - the population of Berlin suffered more Joseph Goebbels, the infamous Minister of Propaganda. In the German capital, he was also an ambitious Gauleiter (District leader). The virulent antisemite wanted Berlin to be 'Judenfrei' (Nazi-German for 'Free from jews') - and he even bothered Hitler with this. On August 19th 1941, Hitler promised the fanatic Gauleiter to 'transport' the jews out of 'his' city when the possibility was there. Only one month later - Goebbels confirmed that this day came closer. In an diary entry of September 24th, he wrote that Hitler stated Berlin would be the very first city to be 'Judenfrei' indeed. The deportations were in sight. Another month later, at October 24th, Goebbels wrote
"Gradually, we start with the evacuation of the Berlin jews to the East. A couple of thousands are already on their way. In first instance, they go to Litzmannstadt (Nazi-German for: Lodz). This causes commotion in the affected circles. The jews ask for support in anonymous letters to foreign correspondents. (. . .) It is annoying that this topic is getting attention in the world’s media, but we have to deal with it. The main thing is that the Reichshauptstadt (Berlin) is made Judenfrei. I will not rest before this goal is totally realised."
. . . Already in this early stage, deportations were connected with the Holocaust. By November 1941 till January 1942, 4000 jews were sent to the ghetto of Riga - where Nazi authorities knew that 'Einsatzgruppen' ('Special Forces') executed these jews.
Nazi Germany pursued the destruction of the Jewish people till the end. They spent enormous amounts of scarce resources (trains, manpower, economic losses) to pursue their evil end. They damaged their own war effort to pursue their evil end of destroying the Jewish people. Why? Hatred. That hatred has infected more than just Nazi Germany.
Sadly, Mein Kampf is a best seller in the Middle East, and is popular in other places as well. There are Muslims with the same goal as the Nazis - destroy the Jewish people. Like the Nazis they are willing to damage their nation to pursue this goal.
The terrorist group Hamas, which forms the government of Gaza, has the destruction of Israel in its charter. They are unwilling to recognize the right of Israel to exist. This is made achieving peace agreements nearly impossible for the Palestinians.
Likewise Iran plans to create a "Palestine" free of the Jewish state and all that implies. At one level this is quite odd when you think about it since Iran and Israel were allies under the Shaw of Iran's government. Israel never did anything to Iran to deserve being target for genocide by Iran. But that was before the Islamic Revolution in Iran. Once Iran was ruled by Shia Muslim clerics, Iran declared Israel an enemy and that it is at war with Israel, the Jewish state. This is based purely on the religious hatred in Iran.
Iran now has missiles that can not only reach Israel, but reach Europe as well. They already have a nuclear warhead design for those missiles, and will soon have a transient and unreliable limitation on its ability to produce the nuclear material to mate with its warhead design to create nuclear tipped long range ballistic missiles. Other Muslim nations, Sunni Muslim nations, see Iran's march towards nuclear weapons and are starting their march towards nuclear weapons as well.
Meanwhile Europe continues to disarm, even in the face of threats from Russia. Russia's ambassador to Denmark just threatened the use of nuclear weapons against Denmark if Denmark participated the missile defense program intended to protect Europe from Iran's threat. What makes this more troubling is that Putin stated a few weeks ago that he was willing to brandish nuclear weapons to take Crimea from Ukraine.
The future doesn't look bright.