If a child tells his mother he was not to blame for the cookie jar being broken, she could still find him culpable if he was the only one home. Culpable means to be at fault.
Culpable is being deserving of blame. If you are culpable of a crime, you are the culprit, or the one who did it. Culpable can be used when looking for the root of the problem rather than a simple who done it. If a teacher leaves the room during a difficult test, and the students decide to cheat, parents might ask whether or not the teacher was also somewhat culpable for the outcome.