You are not appalling! This happens to a LOT of people, honestly.
I have small boobs (A/B cup) and I did feed lying down. It does take a bit of working out but it's worth persevering for that wonderful combo of feeding and sleep!
Perhaps I can try and help. You have to do it on a flat, safe surface like a firm mattress, not a sofa. Lie on your side with the arm that's below you as a barrier between baby and the pillow. Whichever leg is on top is bent, like the recovery position, and to stop baby wriggling down under covers etc. Your upper arm is free to move the baby around but you might need another person to help for the first few times. You're aiming to feed from the boob which is lower down/closer to the bed.
Okay so get your other person to place the baby on her side, facing towards you - tummy to tummy (or tummy to mummy, they say). Lower down than you think - you want to roughly line up her eye or nose with your nipple, not her mouth. Use your upper hand to scoop her in very close to you and pull her down if she's too high up so that - imagine you are sitting and looking up at the ceiling - her neck/head should be in that position relative to her body while she is feeding, so you want the nipple to be higher. Pull HER IN. Don't move your body or your boob closer to her. (You can hold the breast to angle it or use it to stroke her upper lip, but generally you always move the baby to the boob and not the other way around.) It's counter-intuitive but you'll get the hang of it.
You can use the lower arm to prop up your head while you're getting her latched on and into position. Try this when she's calm, not overly hungry, not too sleepy. If you get stressed then it will be harder.
It isn't the most comfortable sleeping position in the world, I got pain in my hips from doing it for too long, but it's perfect for a doze and very safe to accidentally nod off because the baby can't go anywhere, your knee and arm will prevent you rolling over.
It is possible to latch them on by doing a bit of a dangle above them with the top boob but it isn't as comfortable or safe so I would focus on the bottom boob for now. If you need to switch sides, hold baby to your chest, roll onto your back (and then stroke their back and wind them) and then roll to the other side, recreate your feeding position (like a "C") and you're good to start again.
Pulling them close and down is the key, along with tummy to tummy.