Pawsmstter sorry you are going through this. it isn't hard losing a family member. just recently i lost my Congo African Grey Long John Silver, and its still just as hard being without him today as it was the day he left. i believe we will see them all again when it is time. just tell Duke how you feel and that it was an accident.
true story: when we lived in New Mexico we had rabbits. my father had a Jack Rabbit bunny a guy had caught out on the flightline and asked if we wanted it. my father brought it home and he and i made a cage for him out of wood and chicken wire. well somehow the bunny had gotten out of the cage and we put him back in. a few minutes before my brother and i were to leave for school i went to check on the bunny, he had tried to get out again and the chick wire had basically punctured and strangled him to death. this was the first time i had ever lost an animal. though we didn't ahve for very long, it was still shocking. The second rabbit we got, we named him Bugs. (i know real original, right?) we put Bugs outside under a tree we had in out backyard out of the sun. we gave him food and water. my parents went to grocery shopping i was at home with my brother. when my parents came home they finished putting the groceries up and asked how bugs was doing. i went out to check on him...again like you dog duke, he was out of the sun in the shade and he still managed to have a heat stroke. which was kinda creepy because he looked like a taxidermist stuffed him and left him in the cage.
after that we decided to not get anymore rabbit for a while, but eventually found an all black one with white on his paws, that we named Oreo. we kept him until we moved here to florida. before we left we donated or gave him to the zoo there so he could be with other rabbits, because we didn't think he would survive the trip to Florida.
in time you will be able to look back on this and say it was an accident and out of your control. you will miss Duke everyday, and that shows that you truly genuinely cared for him. just take it one day at a time. this is what i am doing over the loss of my bird. one step and one day at a time. i hope this helps some. if not i am sorry, i am not too good at this. i just hope your hurting doesn't last very long.