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/
2. You don't belittle the feelings of others using words like "I'm sorry my rallying cry seemed insensitive" instead of "I'm sorry that my rallying cry was insensitive".
3. You attempt to make amends.
> I feel terrible that my rallying cry seemed insensitive. What I’d hoped would energize the team to meet a challenge we’ve met many times before landed in a way that I did not intend and for that I am sorry.
In other words, I'm sorry that you all took it the wrong way.