You get over feeling like a rotten parent by actively working to change and heal your part of the illness of addiction. YOU go to meetings of alanon or narcanon or families anon. You keep going and you do your best to work the steps and you do all you can to get YOU healthy. Then you will be able to see that cutting off the support to your son was actually not just good parenting - it is GREAT parenting. It is the ugly step that so many people are just not strong enough to take, but you are strong enough.
Think back to when Difficult Child was first learning to walk. He would try, fall down, get frustrated, and then he would cry to get you to pick him up to take him to what he wanted or to move what he wanted to him. You didn't do that. You made sure he wasn't hurt and then you put him down or left him where he was until he wanted whatever it was bad enough to try again and again until he could get to whatever it was on his own.
Now he is an adult but still wants you to pick him up and carry him to get what he wants. Only what he wants is a free ride, no rules or laws to limit him, and someone else to pick up the pieces, clean up the messes and make life easy and fun for him. A good parent is NOT the one who funds it all. The good parent cuts the money off, lets him make his own choices and lets him live with the consequences of those choices, ESPECIALLY when they are ugly. A good parent knows that he won't EVER learn until it becomes too hard and uncomfortable and unpleasant to continue the way he is going.
YOU are that good parent. You are letting him live his life and live with his choices and their consequences. That is what he NEEDS, even if he doesn't want or like it.
In time you will accept this, but it sure is hard to do right now. I am sorry about that.