I'm from Canada (we kinda talk like some Americans), and I can't. Though, I had to Youtube a New Zealander (is that even the term?) to compare the accents. There are not a lot of New Zealanders where I live.
Honestly (and I'm a little embarrassed to admit this) I have a hard time distinguishing between Irish/Scottish/English/Welsh and Australian/New Zealand accents from one another; unless I'm really, really paying attention. Or unless someone throws in a "G'day", or an "Och, aye". Then I can usually tell :P
I think I might be just really bad at accents; a statistical outlier, you might say. Surely not everyone in North America is as bad as I am.