My eighth grade basketball coach said that to us once, only he said, "Indians." Your slang is disrespectful to the American Indian, therefore racist, therefore offensive to the Grand Dream of O'Sensei, therefore offensive to me.
That's a pretty wide racist brush you paint with. What a condescending, presumptive thing to say. What a way to live.
I'm sure you know that calling them "American," let alone "Indians" is the real insult, right?
Is it safe to assume you know the names by which each Native tribe refers to itself and that you use said nomenclature when speaking of them rather than the names given to them by their enemies?
For instance, all of my "Navajo" students called themselves Dine' ("the people"). A few others are:
Apache ("the enemy") = Ndee ("the people")
Comanche ("they fight with us") = Numinu ("the people")
Mohawk ("man-eaters") = Kanienkehaka ("people of the flint")