Right exactly.
This can be generalised easily into a template for a genuine apology:
I'm sorry for doing X - I was wrong. I'll try to do Y better in future.
Note:
- It acknowleges fault, takes personal responsibility and doesn't blame others
- It doesn't make excuses
- It makes a commitment to improvement with concrete action
Everyone makes mistakes. If you think you don't make mistakes or always shift blame onto others you have a problem.
As a fun parlour game, look at this list and think how many of these attributes CEOs you have worked with share https://www.choosingtherapy.com/signs-of-a-psychopath/