Again, however, to try and paint this as being something intrinsic to European dealings with the natives alone would be something of a mistake. Have you read about the atrocities Europeans committed against other Europeans during the Thirty Years War, for instance, or any of the other various rebellions and wars of religion which occurred between Catholics, Protestants, and Muslims in the same era that the European colonization of the Americas was taking place?
To put it bluntly, they'll make your hair stand on end.
This wasn't just true of Europeans either. The Native Americans were just as bad, if not worse, as was just about every other people on earth in that era.
The simple fact of the matter is that it was just a more brutal time in general, where, often violent, authoritarianism was the way of the world, and life was commonly regarded as being rather cheap. In that context, trying to differentiate things in terms of "right" and "wrong" through a modern cultural lens simply doesn't work.
Frankly, there's no more sense in a modern American feeling "guilty" about their ancestors' treatment of the Native Americans, than there is in a modern Italian feeling guilty about his people's treatment of the French under the Roman Empire.
Such events were simply a product of the times in which they occurred. Those times are now in the past, where they should remain.
Celebrate that, if nothing else.