You can see that the dinosaurs (excluding birds) only existed from 230 million (five percent of Earth's full age) and last only a about three percent of that age. Humans appear a mere 65 million years later. Even the first animal life 700-800 million years ago, or about eighteen percent of that age. The first life starts around 3500-4000 million years, when out planet was already close to a billion years old (longer itself than the span of animal life!). This often comes as a surprise even to people who are scientifically educated.
One consequence of this is that dinosaurs were probably as fully modern as today's mammals and birds; they were not "primitive" at all, and weren't driven into exaction by the latter. A large asteroid impact is now the main theory behind the disappearance of non-avian dinosaurs, perhaps combine the mass volcanic eruptions in India. Still, it is puzzling why at least some of the smaller, bird-like dinosaurs didn't sneak through; perhaps a few did (just as a few mammals and birds did) but the quicker evolution of the latter drove them into fossil grounds we simply haven't yet.
More on non-avian dinosaurs (most have feather, like "Velociraptor" (which wasn't) on Jurrasic Park.