That's your call, but I think you'll find zero sympathisers here with your situation. It's VERY clear that N class does not earn miles and it states this clearly on the Asia Miles website.

Did you ever ask anybody if the flight was eligible to earn miles? If not, then it's nobody's fault but your own. If you did ask your travel agent (TA), and they gave you the wrong information, CX will still not give you miles, but at least you can confront your TA about it.

Er, welcome to FlyerTalk, I guess!