I'm not very sure about this, I can't think of a natural-sounding Egyptian expression that could be an equivalent for "feeling silly", but if I use "being embarrassed" I'd say:
أنا مكسوف من نفسي إني محضرتش الاجتماع
Or a regular أنا زعلان إني محضرتش I'm sad/upset
Or أنا ندمان إني محضرتش I regret
I think the English here is much weaker than زعلان، ندمان or مكسوف. It's just an idiomatic way of saying "I thought the meeting wasn't so important and I didn't go, but really I should have gone because so-and-so was going to be there, or they discussed such and such a thing." However despite this person's regret it still seems like it's a "light" issue - the meeting was not that important or that crucial that the absence would cause embarrassment.
What about just والله كان لازم أروح الاجتماع? Or how would you say something like "I can't believe I didn't go to meeting!"? Or maybe "How stupid of me! I should have gone to the meeting!"
Your suggestion is correct. There's also "kan 7a22i/7a22eti ro7t/7aDart el egtemaa3", to which we can also add: ma3leshsh ba2a, elmarra elgayya. (next time, then). This isn't a "promise" to make it up next time, it's just an expression we say.