Responsibility is to be accountable for your actions.
Sometimes people have a tendency to transfer the blame for their actions because they aren't sure how to be responsible for them.
The next time that you hear yourself uttering the words, "Just take responsibility," ask yourself, what exactly do I want to see from my student/child in this moment. When you have that answer, explain it to your student/child in as specific terms as possible.
Although we can not rewind and alter an incorrect behavior, we can acknowledge the role we played in creating the situation, and identify the action we chose that violated the rules of the environment. We can then form a plan that includes a more appropriate behavior for the next time the something of that nature happens.
By helping our students/children to take ownership of their actions, you are empowering them to take control over the outcome of events, rather than serving as the victim to their circumstances.