Actually, as you probably know, many Europeans during the middle ages were killed by mostly the same methods. A number of historians believe the various plagues like the Black Death and bubonic plagues that killed millions of Europeans were brought in from the east or other places outside Europe.
Actually, the Afro-Eurasian disease environment had evolved over thousands of years, with the epidemic diseases mostly evolving from diseases of domestic animals.
These diseases appeared at intervals of centuries, wiping out significant percentages of the population each time. Most of these epidemics are not recorded.
The relevant point is that the Spanish (and everybody else in the Old World) was descended from the survivors of those epidemics, and had acquired considerable immunity as a result.
When the disease ecologies of the two hemispheres merged, the native Americans were within a decade or two exposed to all the pathogens people of the old world had 10,000 years to adapt to. IOW, the Spanish were more highly evolved than the Indians, in their resistance to disease.
It is probable, though debated, that syphilis evolved in America and made the voyage the other way.