To me, that means 1. To identify the issue that occurred (especially when you caused it), and much more importantly, 2. Put systems into place that prevent it from happening again.
Employees can feel very clearly when a manager lacks accountability and as part of mid and especially high level management (if your goal is actually improving both output and quality of people's lives) to not just say you did something wrong, but actually put your skin in the game ensuring what happened will not happen again (usually it means being better at saying no or aggressively managing prioritization rather than heaping additional tasks on people).