I think it was Patrick Collison who also spoke about 'impostor syndrome' when joining YC. I imagine this is probably quite common.
The whole question of what it means to succeed or fail is interesting; OP's perception of failure contradicts what I thought was the common view in SV - that to 'fail' (i.e. not get funding) is part of a greater process of learning and enhancement.
I also can't understand how a 21-year-old Stanford graduate who already has experience in the market he's about to launch in could ever feel he "must have just been lucky".