Apologize fast and the damage stays small. Defend yourself and it grows.

Defending a mistake turns one problem into two. The original thing was finite and probably forgivable, and arguing about whether it happened adds a second injury, which is being told that what someone experienced is not real. An early apology costs almost nothing and a late one looks forced.

When you know you are in the wrong, say so in one sentence, without the word but. Name what you did and what you will do instead. Then let them be annoyed for a while, which is part of it and not a sign the apology failed.