Incriminate or inculpate (oneself)
I don't believe there is a single word in English that can meet all of those conditions, but this is the closest thing I can think of. "Incriminate" doesn't necessarily work outside of a legal context, which is why I would generally prefer "inculpate", but I've never actually seen that word used before - it sounds sort of awkward and artificial, even though it isn't too hard to derive by analogy with "exculpate", a word that actually does see ordinary use.
Also, both of these are actions that could be done to someone else; to make it reflexive you'd have to add the prefix "self-", as in "self-incriminate", but this carries the unwanted connotation of accidentally revealing one's involvement in the matter, while your example is clearly looking for a word that indicates deliberate admission of guilt.
All in all, I think you're better off with "accept/admit + [noun]" (blame, responsibility, guilt, culpability, etc.) instead of a single word.