Apologising to a child teaches something no explanation can reach, because they are watching how adults handle being wrong. It shows that admitting fault is survivable and ordinary, which is the opposite of what most kids pick up elsewhere. It also treats them as a person owed the truth. That lands, and it stays.

Say so simply, and without attaching a lecture, the next time you are short with a kid or get something wrong in front of one. Skip the explanation about how tired you were. Name it and move on.