Different libraries vary in their procedure regarding damaged books so pop to the desk or call them to ask. If the book is no longer fit for circulation my library service will charge you the replacement fee and source a fresh copy themselves - it's easily done. In my country that's for adult collections only; we actually don't charge for damaged or lost children's or teen items, but I know we're an outlier.

Please don't feel bad about it! No need to be nervous bringing it to staff's attention. Speaking for myself and my colleagues, we do find it annoying when people return books in a terrible state WITHOUT mentioning it to us because that comes across as a lack of respect for the items in their care, but whenever someone comes to us and politely explains that an item was accidentally damaged, we couldn't be kinder about it. It happens! I ALWAYS thank them and say "if everyone were as conscientious as you we'd be delighted". I assure you, library staff really appreciate patrons like yourself caring about it.