I have had this discussion with my oldest son, on more than one occasions and at different levels.
We lived in india for a while from when he was 2, and at the time he did not notice that everybody was a lot darker than us, not until we came back home. And that was quite embarassing because we were in a coffee shop at a shopping centre, and he ran off, and he came back dragging a big security guard, who had very dark skin. He shouted at the top of his voice "MUMMY look what I found, he is black" Everybody staring at this little extremely blonde boy....
Now recently after he started school, he came home telling me he didnt want to be friends with this and that boy, because they had such dark skin. I was first shocked, but then I saw it as him actually questioning why they look different, rather than him judging on their skin tone. I took out the pictures from India and showed him photographs of himself playing with, having fun with, being cared for by local people, and also of him at home with friends from India visiting. I told him, look, I am blonde, you are blonde, they have dark skin because where they come from they need dark skin to protect from the strong sunshine. They are your friends and we all really like eachother." etc I did not go into racism, just that everybody look different, blue eyes, green eyes, brown hair, blond hair, red hair, and we are all friends and nice to eachother. I think it worked, as he has now made friends regardless of their skin colour, and his "girlfriend" is mixed race and in is opinion the most beautiful girl in the world.
I agree with the others, a 3 year old is not racist. She is either just echoing what she has heard (and you should try find out where from, but without quizzing her about it) or perceiving he looks different to her and just said " go home" as in leave me (or the toy) alone. Somebody could have said "go home" to her! I am surprised the nursery staff has made such a point about this being racist, clearly they should know a 3 year old cant possibly racist. In my opinion, what goes on in the nursery should be dealt with there, you cant reasonably bring it up with her and ask her about what she meant , most likely she has no clue. But find a book about how we are all different, and read it and talk about it, to pre empt any further issues. Good luck