You know, this actually changes my opinion somewhat.
I still feel that MANY 10 or 11 year olds would be more than capable of sitting with luggage and a younger sibling for a few minutes at an airport. It just does not sound like yours are up to that kind of responsibility yet based on this (and/or that you were gone a LONG time).
I had been sort of assuming the kids had a cell phone on them and called their dad who then asked to speak to the agent. Silly me! I was tired and my mind just went to what would have happened with my kids
If your kids were willing to give out their full names, or other info that allowed the agent to find your reservation, instead of just pointing out which bathroom you were in and telling the gate agent she could find you in there if she had questions, that makes it seem like they are not ready to be left as they were.
I DO think it is good that the girls stayed together and neither went looking for you as some PPs have suggested. My kids were always taught that there is safety in numbers and to stay together in such situations.
Also, I cry easily, and even I think you overreacted in a big way--and a way that is going to shake your little girls and make it harder for them to handle being alone in the future. I can't help but wonder if part of your reaction (crying and shaking at the time and feeling the vacation was ruined by this one little thing) is because there is a little more to the story than you want to share. Were the girls sitting there a LONG time? Did they act scared or did the little one cry for you? (I am thinking if you get so emotional so easily, maybe they did too)? Was the bathroom door clearly visible to the kids? Were the kids seated in an area meant for loading/unloading or otherwise "in the way" and unable to move aside with all the luggage? Etc.