No, you're not an idiot. You're a student who just made a mistake that I'd be willing to bet that you'll never make again. For what it's worth (and from personal experience), screwing up on something...
In any business hourly rate can make it or break it
Do you find presenting your hourly rate to a client can put your client in judgmental state, cause all they see is $$ signs and think
they can get it cheaper somewhere else? Now all they think is so many hours = $$$$
This is after the cost of the project scope was given and more work was required and charged by the hour.