Australia has the worst record of mammal extinctions of any country on earth with about half the world's losses coming from this country in the past 200 years. That's sad but a lot of the cause of losses were from naivety due to late settlement by Europeans and by a lack of knowledge of the unique wildlife, that had evolved so far away from the rest of the world.
Invasive animals have often been involved, though often not as the primary driver of extinction. Often human activity like taking away habitat has led a species to the execution room and an invasive animal might have flicked the switch on the electric chair. That analogy is probably too blame-laden: naivety is usually a big factor, where we haven't realised the problems until it was too late.