Life usually goes on when we disappoint someone. Because we are the center of our own universes, we tend to overestimate our importance at the center of others’ universes. I’m often reminded of this meme:
The ability to cope with change/disappointment is critical to success in life. When someone is totally derailed by a minor disappointment, there’s usually a larger issue that requires attention.
There was probably a valid reason that you had to let someone down, and you probably didn’t make the decision lightly. Trust yourself.
As much as you might like, you cannot be all things to all people, nor everywhere at one time. Choosing one thing means not choosing another. It’s just the way it is.
When you regularly treat others with respect and kindness, small disappointments and let downs are easily forgiven. Be a generally decent human and carry on.