Many factors can be responsible for the obliteration of a species. Even subtle ones. While we, as humans, haven't been resposible for the extinction of even several decimals of a percent of all the past species, I would say that even one extinction is enough. Overhunting is the chief factor in many of these extinctions.
At worst it should have us evaluate our effect on the environment in both biotic and abiotic realms. At best it should prompt action now when the will and education neccessary to avert such tragedies is missing.
I still have some hope that a few Tasmanian Tigers have escaped the peril of extinction. But maybe I've been watching too much MonsterQuest.