The mass extinction event was thought to have paved the way for mammals to dominate, but researchers say many of them died out alongside the dinosaurs.
During the Cretaceous period, extinct relatives of living marsupials - such as possums and kangaroos - thrived.
An international team of experts on mammal evolution and mass extinctions has shown that the once-abundant animals - known as metatherian mammals - came close to extinction.
A 10-km-wide asteroid struck what is now Mexico at the end of the Cretaceous period, unleashing a global cataclysm of environmental destruction which led to the demise of the dinosaurs.
This included more than 90 per cent of species living in the northern Great Plains of the US, which is the best area in the world for finding latest Cretaceous mammal fossils, researchers said.
Metatherians never recovered their previous diversity, which explains why marsupials are rare today and largely restricted to unusual environments in Australia and South America.
Species that give birth to well-developed live young - known as placental mammals - took full advantage of the metatherians' demise.
Placental mammals - which include many species from mice to men - are ubiquitous across the globe today, researchers said.
Researchers reviewed the evolutionary history of metatherians and constructed the most up-to-date family tree for the mammals based on the latest fossil records, allowing them to study extinction patterns in unprecedented detail.
"The classic tale is that dinosaurs died out and mammals, which had been waiting in the wings for over 100 million years, then finally had their chance. But our study shows that many mammals came perilously close to extinction. If a few lucky species didn't make it through, then mammals may have gone the way of the dinosaurs and we wouldn't be here," said Dr Steve Brusatte, from the School of GeoSciences, University of Edinburgh.
