There is an effective way to apologize and an ineffective way.
Here are some ineffective ways:
1. I'm sorry.
That's it. That's it? It's kind of shallow and superficial. If you say "I'm sorry you felt upset," that puts the blame on the injured party. If you say "I'm sorry YOU felt upset," that means you aren't taking responsibility for your actions. That just says you got upset and I'm sorry that you got upset, but it's not my problem!
2. I'm sorry if I did something to offend you.
Ouch. The "if" word is a stab in the heart. It's pretty defensive, and not "owning" it. It's qualifying the apology. Any apology with a qualifier in it is not really an apology.
I particularly remember this one, because I was in a situation where I used this and blew it. I made a terrible mistake early on in my psychotherapy practice. I used this line with a patient. She didn't say anything, but the next week, she came back furious. I guess I was being defensive and didn't realize it. So, even the pros do it.
3. If it will make you feel better, I'm sorry.
Whoa! This one is so insincere that it literally drips insincerity. What you're really saying is "If it will make you feel better (you stupid, weak, annoying idiot), then I'm sorry. Yikes!
4. I'm sorry for whatever I did.
This is one that too many husbands try to use, but then too many wives don't communicate particulars! This one is a bit vague and non-specific.
5. Any and all apologies followed by the word "but..."
This apology reminds me of a funny thing that happened in a psychotherapy session. I sometimes get a little playful with words and images, so when I had a husband and wife in therapy, and every time the wife opened her mouth, she said "but, but, but, but," I said back "you're a 'but' with feet!" She went through the roof, because she thought I called her an ass. I guess I should have watched the way I worded that comment. I wasn't sensitive and got a little too playful at the wrong time.
That example segues into how to apologize correctly
First of all, you personalize your apology. "I am sorry I hurt you."
Anything that is personal is felt more deeply. That needs to grow into "I'm sorry I hurt you by breaking my promise...."
or whatever you did.
The third part of the apology occurs when you show you really understand why this was upsetting - you're not only acknowledging that it was upsetting but also why it was upsetting. "I'm sorry I hurt you by breaking my promise to call."
You are justifying their being upset. You elaborate on all the hurtful aspects of what you said that you're aware of, and then you again express regret and remorse. "I am so sorry I have hurt you. I take full responsibility. I did this and I regret it. I have remorse. I was being selfish and flighty. I was insensitive."
It's really then important to express some desire to make amends. Discuss what you are going to do inside your heart, soul, life, mind, and habits to make sure it doesn't happen again. And repeat your apology as often as needed, especially for bigger wounds.
After things have settled down, and some time has gone by, you might want to talk about some mitigating circumstances, but in general, I wouldn't suggest you go in that direction until the pain has subsided to a much lower level. And don't use the excuse "I had a few too many drinks."
You still did what you did.
If you are going to apologize, make it sincere or don't bother.