As an English speaker, I doubt I would ever say 'the blame is on me', unless some agent was specified as putting the blame on me. Perhaps 'I am to blame'.
I wrote 'it is my fault', but it was not accepted. Isn't this what the sentence means – that I am responsible? Or is the implication that I am being blamed, perhaps unfairly?
That is not a "more correct" translation, it is simply an alternative.
Unlike many of the other "direct translations" of emotions or states, such as brón or ocras, "the blame is on me" is a perfectly normal construction in English - in fact, it could be argued that the "to blame" construction is the more unusual construction in English, without any obvious parallels, whereas blame, responsibility, duty, etc can all be "on" somebody.