Because the asteroid didn’t obliterate the earth, it just destabilized the climate and ecosystems that supported the dinosaurs to such an extent that they couldn’t survive. It took a massive amount of vegetation to keep the leaf eaters alive, and a massive amount of those to keep the sharptooths alive. As cold blooded animals, they also had to deal with intentionally regulating their body temperature, something a massive asteroid would have made more difficult.
Mammals and other small creatures on the other hand did not face these same challenges to the same extent as the mega lizards did. They could survive on smaller portions of food, in more diverse areas, etc.
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