In fact, finches aren't even mentioned in On the Origin of Species. While the finches are covered in his journal, he seemed to be largely confused by the appearance of the finches on the different islands. He speculated that the finches might have come from one common ancestor, but never finalized an evolutionary hypothesis based on these birds.
Additionally, he barely tracked said finches on the islands--he didn't label where he found the specimens he took, hardly spent time observing their diets, and was confused by the significance of their beak types. He didn't know enough about the finches to cite them in his book, and they definitely didn't convince him of evolution.