In ancient Greek and Roman religion the statues and temple buildings themselves were not the foci of worship. The buildings that we think of as "temples" were not, in fact, temples, they were treasuries used to store the gifts given to the temple. The temple was the sacred precinct called the temenos/templus(hence the word), frequently enclosed by a wall or some sort of physical marker. Within the temenos/templum, the focus of worship was the altar, everything else was window dressing.

For example, the most famous ancient "temple" is the Parthenon, but there isn't actually much of the way of evidence that it had any real ritual function. The altar on the Acropolis was associated with the Erectheon, which housed the xoanon, which was a type of aniconic wooden figure that represented the god. Xoana were actually quite important to religious devotion and frequently had mythological origins (I believe the Parthenon's fell from the sky), big flashy statues were not. It I had to make a comparison, it would be something like the difference between the Shroud of Turin and the ceiling of the Sistine Chapel. The latter is big, beautiful, widely admired and loved but is not itself sacred.

This gets a bit more complicated when dealing with the Roman Lares and Penates, which may have been Etruscan in origin. These are generally said to be deeply personal gods of a household or specific family, frequently placed in a niche in a wall by the kitchen. But there were also Lares of neighborhoods, military regiments, and collegia. But here again the figures are not themselves actually worshiped, rather they are the focus of worship.