Which major extinction event? Do you really think this is an appropriate comparison to proven major extinction events of the past (e.g Chicxulub, 66 m. years ago)?
New Zealand was the same. Humans arrived around 1300 and we lost the moa and Haarst's eagle (the world's largest flying bird) by around 1400.
Incidentally, the largest species of bird that ever lived was the elephant bird of Madagascar. It weighed up to 730kg (1600lbs) and stood 3m (10ft) tall. It went extinct around the year 1200.
There used to be a lot more interesting animals around, but our ancestors hunted them to extinction. Nobody misses them because nobody alive today ever had them in the first place.
It's sad, but even the extinctions of the coolest, most amazing creatures are quickly forgotten. When the giraffe or blue whale is gone, it will just be another story like the elephant bird.