“Mistakes were made” is how people apologize without being in the sentence.

Some apologies are built so the speaker never appears in them. Something went wrong, errors occurred, things were handled poorly, and no person ever turns up as the one who did it. The listener hears the shape of an apology and still has nobody to forgive, which is why those sentences leave everyone unsatisfied.

When you apologise, use your own name or the word I, and say the specific action. One sentence with you inside it does more than a paragraph of passive regret. Catching yourself writing around it usually means you have not fully decided to own the thing.