Two elements of an apology
Compassion and Contrition
"We're sorry that your flight was cancelled. This must have truly messed up your day, sir."
That's a statement of compassion.
"Cancelling a flight that a valued customer trusted us to fly is not the way we like to do business. We messed up, it was an error in judgment for us to underinvest in pilot allocation. Even worse, we didn't do everything we could to get you on a flight that would have helped your schedule. We'll do better next time."
That's what contrition sounds like. We were wrong and we learned from it.
The disappointing thing is that most people and organizations that take the time to apologize intentionally express neither compassion nor contrition.
If you can't do this, hardly worth bothering.
But it is worth bothering, because you're a human. And because customers who feel listened to help you improve (and come back to give you another chance.)