A Little Girl called me a 'Nigger' Today...

As I walked past a house a young child, probably 7 or 8 years old, white with blonde ringlets, jumped around near the front gate and then stopped. And looked at me with a fierce expression. I half smiled and as I walked past her I heard her say, 'Nigger!'
It stopped me in my tracks as I thought of how much poison had probably been poured into this child for her to see me, a black woman, as nothing more than 'a nigger'.
In that split second my mind raced around for me to decide on some proper response, be that to walk away and say nothing as this child is a product of her environment; or say something to the child, but what exactly? Was it offensive to me and if so why? What could I say to the child that would be age appropriate?
What did I do? I walked back to the gate and said, 'I'm sorry but I heard that.' She said, 'Heard what?' and then it hit me that I was doing the wrong thing, talking to the child about it was not correct. It didn't feel right.
I almost called out to the shadowy adult who could be seen through the multi-coloured strips hanging at the open front door. Then I walked away. As I walked on she shouted, 'I never called you that word!' She knew and I knew and I felt sad. 

Is there a 'right thing to do' in this situation?