Romans had a different standard of civilized than we do. From Judeo-Christian society's view that all life is sacred, their act of throwing people to the lions for entertainment and barbarians having people fight animals or just mauling the bodies seems just as bad.
From the Roman's perspective, civilized people had control over their emotions, they were more rational. Think of the Cynics who valued being in total control, never surprised, never irrational. So if they watched someone get ripped to shreds in the arena without getting excited or ill or angry, they were civilized while the barbarian begged for his life or screamed at the monsters circling him.