Genocide as a concept, i.e. attempting to exterminate people of a certain race didn't really appear until the 20th Century.
But genocide is not only defined as the simple extermination of all members of a group of people. It can also mean the systematic destruction of their cultural and ethnic identity. Forcing them to assimilate into another population. That form of genocide at least, is very common throughout history. By the time of the fall of the Roman Empire, how many citizens of Italy considered themselves to be Etruscans? Or Samnites? Or Ligurians? You don't need to kill everyone in order to destroy a people. In fact, that's probably the least efficient or effective way of doing it.