The standard here seems to be drop and run from reception (5) onwards. I have occasionally been asked if I need help (which I thought was very sweet) but always said no as our house is too small to accommodate the extra parents and siblings.
The most I have had is 13 over excited six year olds in a small house. (Planned to do lots in the garden and then it just poured down all day). But we managed by putting a massive tent up in the garden and doing games and disco in there. It was hard work for me and dh (esp with 6 month old to bf while serving food and drink).
I don't have family nearby but would find it very hard to do it on my own/without dh. We have one person on entertainment/ herding duty and one on food/drink/toilet issues etc.
I wouldn't expect other parents to help as that's not generally the norm here. But on the other hand I probably wouldn't do a big group of any age without back up of some sort - paid or otherwise.
Maybe next time do a smaller group or if you can afford it, a venue where the staff give proper help. I agree that 11 year olds can be enlisted to help with serving food and drink. I've had 6 year olds doing bits (just helping themselves to juice cartons etc) and have nephews who are 11 who are v good waiters 
But I think people are being a bit harsh to say oh I'm a teacher and I can handle massive groups or why couldn't you handle it. Teachers are obviously amazing at dealing with groups of kids but not everyone has had a lot of experience and some find it very tough.
Sorry you found it so stressful OP
but think YABU to blame parents for dropping off.