This section of the FAQ has some threads on the subject.

The same thing did happen to Europeans. The main difference is that the colonial populations were allowed to recover while the indigenous populations did not.

Native societies were certainly more susceptible to epidemic disease than Europeans, but the sudden drop in population led to major power imbalances that led to prolonged periods of warfare and slave raiding that prevented populations form recovering (in North America at least, not sure about South America). Their villages, fields, and population centers were constantly exposed to outsiders of dubious intentions and the prolonged and widespread fighting further spread diseases around and led to recurring outbreaks from which those societies often could not recover.

European colonies in North America were more used to epidemic diseases, but death from disease was still enormous. The trans-Atlantic slave trade introduced African disease from which the Europeans had little exposure prior to the 17th century, like yellow fever and malaria. Early settlements like Jamestown and Plymouth had ridiculous mortality rates from disease. Death by disease was so common that Virginia people who did not died young could end up marrying and remarrying 4 or 5 times. Infant mortality was also very high. Death tolls were highest among recent immigrant populations, who lived in worse conditions and did more dangerous work. Caribbean and Southern colonists referred to those who survived the first few years as seasoned. We don't have exact numbers, but as few as half of the earliest waves of colonists lived long enough to become seasoned.

The main difference is that, because European colonies were less exposed, they were far more likely to survive once they made it past ten years. They were coastal and had fairly direct access to European goods, guns, supplies, and (most importantly) replacement populations in the form of new immigrants. The ocean prevented them from being attacked from behind by anything but another European power and they formed close trade relations with those indigenous peoples with whom they were immediate neighbors. Those indigenous peoples often relied on European guns to fend off rival tribes, but they're proximity to the colonists made them more vulnerable to diseases and to dispossession by the land-hungry colonists. Those neighbors in turn buffered the Europeans from attacks by more remote tribes. Some of the local tribes ended up turning on the colonists, but the colonists were too well-entrenched to be expelled by this point. Thus, while Europeans could be weakened by disease with frequency, the nature of their settlement patterns made the settlements less vulnerable than indigenous settlements, who were afforded less opportunity to recover from the epidemics.

Sources:

• Shannon Lee Dawdy, Building the Devil's Empire

• Elizabeth Fenn, Pox Americana: The Great Smallpox Epidemic of 1775-82

• Nancy Isenburg and Andrew Burstein, eds., Mortal Remains: Death in Early America (edited collection)

• Erik Seeman, Death in the New World

• Edmund Morgan, American Slavery, American Freedom: The Ordeal of Colonial Virginia

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