Job offer/pay question.. did I mess up?!

I applied for a management position job and was offered the job. I accepted but they said details, pay, etc will be discussed when I receive the paperwork. I feel nervous because on the application in salary desired I just threw down a random number so I wouldn’t feel like I’d be asking too much. Now im afraid they’ll start me at a low pay grade but I know my assistant is only making 11.75...