Blame is a dead end. Responsibility clears the way for action.
Blame is all about whose fault it was. Responsibility is all about repairs and/or amends, restitution and/or apology. In short, blame is about the past and responsibility is about the present and future. Since the past cannot be changed, blame is of very limited value. Assigning responsibility changes the present and so affects the future.
It is true that blame has its uses. Some things cannot be fixed, amended or repaired and as a society we find them to be beyond apology. Then we affix blame and assign punishment. Yet we often use blame to avoid responsibility. We find a scapegoat to blame for our own mistakes, or, for example, blame the President for the deeds of those who hide behind the mask of a corporation. We often blame others when they reflect parts of ourselves of which we are ashamed. Misplaced blame is an enemy of personal growth.
Accepting responsibility is empowering. Assigning responsibility expresses confidence that the recipient will rise to the task of making things right. Sometimes we find that we must accept responsibility for another's misdeeds or mistakes. We have a choice then to feel persecuted, wrongly required to clean up someone else's mess or we can feel empowered and entrusted to be the hero and make things right.
I wish you peace in your quest to rightly decide whether it is blame or responsibility that needs to be assigned.