At the time (and about the time) Harper Lee wrote To Kill a Mockingbird, justice was reserved only for white people. The story illustrates this point: Tom Robinson, a well-known, upstanding black man is proven innocent in court--he could not have possibly done was he was accused of doing--but he is quickly found guilty and sentenced, anyway, because he has been accused by a white man. It doesn't matter that the white man--Bob Ewell is not a man of influence or power. He is described as a low-life who lives off the county and is despised by all of Maycomb. Nevertheless, no jury of white men will fail to find a black man accused by a white man innocent.
Incidentally, this is still true to a great extent today: African Americans accused of crimes are convicted at a considerably higher rate than Whites accused of crimes, and the African Americans serve considerably longer sentences. The problem did not magically go away with the Civil Rights Act.