Almost everyone in Europe at the time were of European stock. Any Latinos who were in Europe at the beginning of the war would most likely have been in Spain, which was neutral. Asians did not represent a significant minority in Europe then, even the ones from the USSR (like people from Mongolia). Many European nations had colonies in Asia, but most colonials stayed at home in their native countries. Probably the largest population of the people you've asked about were black people. Italy had colonies in Africa, as did France, though both included both Arabs and black people. There just wasn't a significant presence of blacks, Latinos or Asians in Europe when Hitler went on his rampage.
There were other people put in concentration camps, however. They included: priests and religious people (one Catholic friar from Poland, Maximilian Kolbe, who volunteered to take someone else's punishment and died, was later canonized by the Catholic church and is now a saint) who spoke out against Hitler or who preached against his policies on moral grounds; political dissidents who disagreed with Nazi policies and practices, or who angered Hitler in some other way; those with disabilities, both mental and physical who had not been eliminated by the medical killing program; ethnic Poles, Slavs, Russians, and others considered physically and genetically "inferior"; Allied prisoners of war, especially those caught at the beginning of the war; regular citizens considered a threat to the Reich, like intellectuals, educators, doctors, and scholars; foreigners suspected of being spies; resistance members from all countries; and members of the Nazi party or other German organizations who had fallen from grace for one reason or other.
Basically, anyone considered a threat to the Third Reich, and not just for genetic reason, was stuck in a concentration camp. In some cases it was so they couldn't spread their "inferior" genetic material, but in other cases, many cases, it was because they spoke openly about their disagreements with Nazi policy, or because they presented a real threat as enemies of the state. Many people were executed outright, but many others were simply put where it was felt they couldn't do any harm or interfere with what was going on.
The largest group of non-Aryans living in occupied Europe during the Third Reich were the ethnic Jews, and we all know what happened to them. Hitler attempted to wipe them off the face of the Earth.
And just so you know, while they weren't Nazis, there were Asians in Wehrmacht uniforms captured during the D-Day invasion in June of 1944. They were originally in the Russian Army, and were captured as POWs in the East. A lot of the beach defenders at Normandy were Ost soldiers, meaning they'd been captured in the East and forced to wear German uniforms and fight in the West to defend German interests. Most of them were Poles, or Slavs, but there were several Asians taken prisoner. It surprised the Allies--they were very puzzled about how Asians ended up defending the Atlantic wall. That was a bit of a miscalculation on the part of the Germans--using prisoners who were considered inferior was a bad move--a lot of them surrendered as soon as possible, either when the Germans who were forcing them to fight were killed, or when they killed them themselves.
I hope that helps explain it a bit for you.
WWII is of particular interest to me