If your apology needs a paragraph of context, it’s turning into a defense.

Every line of background you add moves the weight from the thing you did towards the circumstances you were in. The context may be completely true, and it still has the effect of asking the other person to feel differently about your part. By the end they are being invited to understand you rather than to be heard.

Give the apology on its own, with nothing attached, and let it sit. If they ask what happened, tell them then, as a separate thing. The explanation keeps perfectly well for half an hour.