I read an interesting paper several years ago that theorized that the super heated gases and ejecta from the meteor impact would have caused world wide infernos that destroyed most edible plants, especially in North America, which had the largest and most diverse concentration of dinosaurs in the world.
When the plants die, the herbivores die, and when herbivores die, the carnivores die.
True, but furry little scavengers and seed eaters can get by for a while.