Let me explain further.
Most people's idea of religion today is belief in a sacred text. Judaism, Christianity, and Islam, for example, all have sacred texts at their core. Greek (and Roman) religion was completely different. There were no sacred texts; worshipping a god consisted of making offerings and carrying out prescribed rituals at certain times. There was no equivalent of the Bible in Greek or Roman religion.
Greek mythology served a completely different purpose. Ancient Greece, as I'm sure you know, was not a single country, but consisted of numerous independent "city states" - Athena, Sparta, Corinth, Thebes, and so on. What Greek mythology (which was the result of centuries of oral story telling and poetry) did was to provide an important element of Greek cultural identity. No matter if you were from Athens or from Thebes, you were brought up at your mother's knee with this body of stories, and that was an important part of what made you "Greek". Many of the stories were about the gods, yes, but they were not a part of "religion" because, as I've explained about, texts played no part in religion.
Does that make it any clearer?