Not my area, but I think you need to go back much further than the dinosaurs for a common ancestor. I'm sure someone with actual knowledge will educate us in the comments.
Humans and dinosaurs have a common ancestor, but it's further up the tree than the dinosaurs. Mammals broke off from the reptile tree so whenever that split happened, that's who you're looking for. If you want to follow this train of thought further, we are all from the same primordial soup of bacteria. You me the birds, the bees, the bears, all of it.