The SD may not even know you couldn't get off of work. someone probably ran up to her and said "DavinciSoprano cancelled." You know how it is at comps, the SD is too busy to really hold long discussions. She might have even learned by text message. Cut her some slack.
As for the comment "we're glad she did." It probably meant that they were able to find someone to take the slot at the last moment. People are having conversations in their head about what they're about to say when making announcements (bec. they're nervous) and it makes sense to them, but may not mean what the speaker means to say. It takes a LOT of training to make off the cuff announcements that are a. short, b. sensible, c. say what's meant to be said. I bet your SD doesn't have that kind of training.
Go to the SD, tell her that "Sorry, I couldn't get off work in time for the Improv. I'm glad you were able to find a replacement at the last minute. That was good organizational planning on your part." You left her hanging (it wasn't your fault) but she still needs some affirmation that she did a good job, which it sounds like she did. In your twenties it's time to put on the big girl armor and learn to roll with the punches. In the big girl world, no one cares if your feelings are hurt. My experience is to never tell anyone at anytime they hurt your feelings, unless they are a close personal friend.
Man, I can't tell you how many personal and professional disappointments I've had in my 60 years of life. I don't put much emotional investment into stuff like that any more. People say what they say. Roll with it, baby, roll.