Actually, Native Americans were used by European colonialists as slaves some time before the transatlantic African slave trade began. As well as being a method of economic exploitation, enslavement of indigenous peoples was used as a weapon of war, a convenient way of clearing vast swathes of land for white European settlement. It's estimated that in southern coastal regions, entire tribes were wiped out through slavery, far more than perished from war and disease.
Every European nation that colonized the Americas used native slave labor for construction, plantations, and mines. Primarily, though, indigenous people were exported to colonial outposts in the Caribbean. Over time, however, Native Americans gained the reputation of not being very suitable slaves. For one thing, they proved remarkably adept at escaping if they weren't enslaved too far from their ancestral lands. As for those enslaved people exported to the Caribbean, too many of them died on the journey, succumbing to European diseases. By 1676, Barbados had banned Indian slavery altogether—not on humanitarian grounds, but because it was simply too much hassle for colonial authorities and slave-traders alike.