Hey there! There is a discard mechanic if you drag cards from your hand over the discard pile. Let me know if that isn't working for you!
Sorry that I falsely accused your game of having no discard pile, to be honest I didn't even notice it before and just thought the small card with the X meant it was a used card, not a discard logo. After I saw your reply, I just tried to put a card over anything I could and I eventually found it. Again sorry for the confusion, but I did get rather unlucky with the ethereal pack