Everyone makes mistakes. You are not alone. I jokingly tell people "I made a mistake once...
...and then I stopped counting." I'm glad I stopped counting. I have made too many mistakes to dwell on them. I have gone back and figured out what I could have done differently so I would not have hurt someone. Sometimes that works.
There are methods for offering a sincere apology posted on Psych Central. If interested see here
psychcentral.com/blog/.../how-to-make-an-adept-sincere-apology/
psychcentral.com/.../7-ways-to-give-an-apology-4-ways-to-accept-one/