There is no evidence that the Greeks worshiped the titans. The succession described in myth does not equate to a historic stratigraphy of belief in the Greek peninsula. The Olympians replaced them in myth but not in religious practice of the Greeks themselves.
Throughout Europe it was common to have a pantheon of gods who were the successors of an older race. This previous generation of supernatural beings were invariable gigantic and they played a role in the creation and/or ordering of much that existed in the world. As late as the nineteenth century it was not uncommon to hear Europeans tell stories of how that rock fixture or this ancient structure was built by a giant.
European legends dealing with giants were generally etiological, meaning that stories were told to be believed and were intended to explain the origins of things, typically features in the landscape or old structures. The name of the Giant’s Causeway preserves the idea that an enormous supernatural being built the path to walk from Ireland to Scotland. Wade’s Causeway, is another reference to a giant, in this case to explain a Roman road in Yorkshire. The etiological role of giants was paramount but the explanation of the landscape, megaliths, or even extraordinary buildings often merged with those of trolls and even the devil. For example, the Devil’s Dyke in Cambridgeshire is an example of Satan affecting the landscape in a way normally reserved for giants.
We can look to these stories to understand, by analogy, how the Greeks likely viewed the titans: they and their monuments were awe-inspiring but the supernatural beings were never an object of worship. They belonged to an earlier time, they were defeated, and their successors were the only ones who warranted devotion.