The reason why there are no dinosaur fossils at the La Brae Tar Pits is simply because the dinosaurs had been extinct for 65 million years before the tar ever reached the Earth's surface. The tar pits at La Brae formed about 50,000 years ago, during the last Ice Age. This was during the Pleistocene epoch, which is the geological epoch that directly preceded our current one. This was an age of large mammals. Giant sloths, mammoths and mastodons, dire wolves, saber-toothed cats, and more roamed the area during the Ice Age. That is why most of the bones and fossils excavated from the tar pits at La Brae belong to these now-extinct creatures. The dinosaurs were long gone by then.
It was the tar itself that trapped so many creatures in the pits. When animals became trapped in the sticky tar and died, their bones were perfectly preserved. This tar formed deep under the planet's surface but did not reach the surface until the Pleistocene epoch, long after the dinosaurs. Therefore, there would not be any creatures that lived before the Ice Age in these pits.