Apologies often do not work.

The person who was offended may have very minimal confidence in the apology. Most people are not as needy of an apology as they are to feel understood and respected. In fact, it is likely that the only way apologies help – the only time they do work – is if by showing regret, the aggrieved person feels that you respect and understand the pain you caused.
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First ask how you hurt them and show concern. Don’t offer excuses or defenses. Instead, understand how much pain you caused by looking at it subjectively – how it felt for the other person.

The next step after listening is to repeat what you heard – in your own words – without making any excuses. Just express that you respect and care about how much pain you caused. At that point, you could use the word “sorry” or “apologize”, and it will be far more effective.

Lastly, state what you will try to do differently in the future, so that this doesn’t happen again.
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Own up to what you did: Think it in first-person. And then say it in first-person. And in active voice (not passive). “I am sorry that I left you waiting for 15 minutes.” Not “I’m sorry that you were waiting for 15 minutes.”

Acknowledge how you hurt the other: Show that you acknowledge how whatever you did, or didn’t do, has impacted the other person. Validate the other person’s feelings of hurt or anger. Show them that you care about how they feel. “I recognize that my coming late inconvenienced you and the family.”

Resolve not to do it again: Learn a better way to handle whatever it was that preceded your offensive action/words. And say it aloud to the other. Telling the other your resolve for the future is more than just part of the apology; it’s also something of a self-fulfilling prophecy. Be as specific as possible. State this resolve in positive terms – what you will do differently – rather than what you won’t do. “I will be more careful…” rather than “I will not be so careless…”

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Excerpted from Marriage 911, Rabbi Simcha Feuerman, LCSW-R and Chaya Feuerman, LCSW-R authors.