And were Native-American slaves brought to Europe?
Your question is a bit difficult to answer without a time frame and with respect to which cultures we are talking about. It is true that, for a time, there were more Native American slaves than African slaves in North America. I'll quote from a previous post I wrote about the Indian slave trade in North America for most of the rest of this answer.
The traditional narrative of the Americas after contact grossly neglects the influence of abduction and slavery on Native American populations. Both small scale abductions, and large scale slaving raids, were used by European populations to turn a profit, reduce resistance to territorial encroachment, and as a tool of war.
Before first contact with officially sanctioned entradas to Florida in the early 1500s, unofficial traders and fisherman plied the Atlantic and Gulf Coast. These unofficial voyagers routinely augmented their stores with unwary captives, either for sale as slaves in the Caribbean or Europe, or to serve as translators for later voyages. During the first official entrada to Florida in 1513, the Spanish encountered Native American populations along the coast that already understood a few words of Spanish, and fled from the new arrivals, leading Juan Ponce de León to assume slaving raids preceded his arrival. When Verrazzano explored the Atlantic Coast in 1524 he encountered coastal populations who refused to trade directly with Europeans, preferring instead to exchange goods boat to boat across a line, possibly in an attempt to keep their distance and prevent abduction. Tisquantum/Squanto was subject to several of these small-scale abductions along the coast before he returned home and encountered the small English outpost at Plymouth.
Abductees were routinely sold in either the Caribbean or Europe, or trained as translators for future conquests. Accepted Spanish policy for new entradas included an initial journey to abduct a few young men, train them as translators, and return a few years to conquest and establish missions. This method was used to great success in Peru, when Pizarro captured two young boys from the coast in 1528. One of the young men, Martinillo, served as a translator during the famous showdown in Cajamarca in 1532 that resulted in the capture of Atahuallpa. In another example, Don Luis, a young man abducted by Spanish missionaries in 1561 from the Virginia tidewater region, returned in 1571 with a party of Jesuit fathers hoping to establish a mission near the James River. He escaped, organized the martyrdom of the Jesuits, and later advised Wahunsenacawh/Powhatan to expand the Powhatan Paramount Chiefdom to oppose Spanish encroachment. Wahunsenacawh/Powhatan’s daughter, Matoaka/Pocahontas, would later travel to England in 1616 where she was presented to the King James and Queen Anne as the daughter of “the most powerful prince of the Powhatan Empire of Virginia.”
Large scale slaving, and slaving raids, became a tool of war for English once they began to establish permanent settlements in the New World. The peace established between Plymouth and the Wampanoag lasted a generation. Massasoit’s son, Metacomet/Phillip, succeeded his father as sachem and due to a variety of factors organized the hostilities now known as King Phillip’s War. When the dust settled more than 3,000 Native Americans were killed and hundreds of survivors who were not professing Christians were sold into slavery in Bermuda.
The Carolinas used slaving raids as a tool of war against Spanish Florida, as well as a means of raising capital. Traders employed Native American allies, like the Savannah, to raid their neighbors for sale, and groups like the Kussoe who refused to raid were ruthlessly attacked. When the Westo, previously English allies who raided extensively for slaves, outlived their usefulness they were likewise enslaved. As English influence grew the choice of slave raid or be slaved extended raiding parties west across the Appalachians, and onto the Spanish mission doorsteps. Slavery was another aspect of warfare, and the English attempts to rout the Spanish from Florida included enslaving their allied mission populations. Slaving raids nearly depopulated the Florida peninsula as refugees fled south in hopes of finding safe haven on ships bound for Spanish-controlled Cuba (a good slave raiding map). Gallay, in Indian Slave Trade: The Rise of the English Empire in the American South, 1670-1717, writes the drive to control Indian labor extended to every nook and cranny of the South, from Arkansas to the Carolinas and south to the Florida Keys in the period 1670-1715. More Indians were exported through Charles Town than Africans were imported during this period.
In both acts of small-scale abduction, as well as organized large-scale slaving raids, slaving often served as the first shock of contact between coastal Native American populations and European arrivals. The repercussions of slaving raids spread far in advance of European settlers, shattering previous lifeways, and sparking the rise of powerful confederacies like the Creek, Choctaw, Chickasaw, and Cherokee to combat slaving raids.
As for why we don't recognize the sufferings of Native American slaves, well, that is a complicated issue and one I have only a few guesses as to why. Until recently, public consciousness tended to generally ignore the influence of Native Americans in North American history. Their presence in the slave trade is folded into that general historic amnesia. Second, the sheer scale of the African slave trade dwarfed the Native American slave trade after ~1700.
As you can see, the slave trade was a major factor influencing Native American population dynamics after contact. Though disease is the common explanation for Native American population decline after contact, in some places, like the U.S. Southeast, there is reason to believe excess mortality and population loss due to slaving raids may have had as much of an impact on population decline as introduced pathogens.
I suppose that might have been initially true if you count all the Native Americans that were ever enslaved, but virtually all Native American groups suffered something like 75-95% population decline within a generation of European contact, due to diseases, mistreatment, social breakdown, etc. Which means that there weren't too many Native Americans to enslave once contact was established, and those enslaved by whites don't last very long due to disease.
On the other hand African slave populations grew continually and were prized above others to their resistance to malaria, so in the long term it was much more profitable to enslave Africans than Americans.
Plus the Spanish crown declared that the natives cannot be enslaved, so I don't think that assertion is officially true, although their treatment is probably on the level of slavery in actuality. If you count all the native subjects of the Spanish territories as slaves, then the assertion makes sense due to the sheer number of natives living in those areas, but otherwise I doubt its veracity.