Veneration of Mary does come up as a topic in Luke, though not in a way that makes it immediately plain why there are statues of Mary in most Catholic churches:
While [Jesus] was speaking, a woman from the crowd called out and said to him, "Blessed is the womb that carried you and the breasts at which you nursed."
He replied, "Rather, blessed are those who hear the word of God and observe it."
Is this a rebuke to those who would venerate Mary? I see it, not as a rebuke, but as a correction or clarification to the woman's words of praise that serves three purposes.
First, it shows that any honor Mary might deserve from Christians is due her first and foremost because she heard the word of God and kept it. (Which, after all, is pretty much what we read Luke's infancy narrative, and in the earlier report of the visit of Jesus' relatives.)
Second, it shows that an honor similar to that of Mary is available to anyone who desires it, simply be hearing the word of God and keeping it.
Third -- and this is an idea I'm stealing from a coincidental email from Kathy the Carmelite -- it guards against veneration of Mary on purely physical grounds, or indeed on any other grounds than fidelity to the One God. Of all creatures, we value Mary the highest, but not for what she is in herself (and still less for any "sacred feminine" some claim she signifies). We value her entirely for what God has done through her, even as the ways in which we express the value we assign her necessarily adopt incarnational dimensions. Her womb is not blessed because it bore Jesus; her womb bore Jesus because God blessed her, and through her each of us.
This principle holds, even when particular Catholic practice improperly loses sight of the principle.