And our ancestors at the time were the early mammals - smaller, rat-like creatures, and a few other species. They were mostly scavengers who were better able to survive the difficult conditions, while many other animal and plant species died.

As things got better, without giant lizards stomping around everywhere, those mammals were able to thrive, diversify, and spread all over the world into the wide array of mammals we have today. Including the first primates, somewhere around 55 million years ago (well after the meteor extinction event), who would eventually (millions upon millions of years later) give rise to us.