I feel racial slurs are evidence of racism, but do not constitute racism of themselves.
For instance, a racist man could just as easily call a black person a cunt as a nigger. The reason he would tend to use the latter term is because he wants to make the black guy feel as bad as possible.
On the other hand, someone who holds no actual racist beliefs may call a black guy a nigger in an argument or a fight deliberately to annoy or intimidate him.
The upshot: causing offense with racial slurs is not the same as 'racism' in terms of belief that members of one race are inferior.