Failing at your own startup is a bit like burying a child. You start with all these dreams of a bright future, and one day you find yourself facing the stark reality that it just didn't work out, that there's nothing you can do anymore to change that, and that basically the last X years of your life, where you sacrificed anything, were pretty much for nothing. "Well, at least I learned a lot!" is very little consolation in that context.
It's a pretty fucking tough time to go through, burying your startup. I've been there, and hell, I'll probably get there again some day, but it's not the kind of thing that you go through without after-effects.
As a startup employee, you're a bit like that neighbour who watches the previously happy couple tear each other apart and finally divorce. My, ain't it tough for them, geez, I hope it never happens to me.
As the founder, you're right in the middle, ripping your dreams to bits.
And the best part is, after all that, people still expect you to pick yourself up and do it all again!
Edit: I suppose I'm being a bit melodramatic here, as pointed out by the two responses. That said, I do think that shutting down your failed startup that you poured your dreams into is a deeply demoralising experience. Character-building stuff, I think they call it, when trying to cheer you up.