The whole job market can be very demoralising, but it really is a numbers game (assuming you're looking for retail/hospitality/entry level jobs), and getting your first one is hard because you don't have experience.
You are being too hard on yourself - you have done well to get to the interview stage, and that in itself is useful experience. It's not like school where, if you have the ability and work hard you will get good grades. In an interview you have no way of knowing how good the other candidates are and their attributes and experiences are completely out of your control. Usually all/most of the candidates selected for interview could do the job and do it well, but the employer is only looking for one of two and they will look at things like experience or how each candidate would fit into the existing team. None of this is a reflection on you, and if your parents are employed themselves, they should know this.
It might be worth looking at volunteering to increase you experience in the areas you want to work. An afternoon a week at an Oxfam shop will teach you how to use the till, stock control, customer service skills. Equally there are lots of volunteering opportunities in education, care/health, environment etc and as you're 18 you shouldn't be restricted in what you can do, and it might be a welcome change. Looking for seasonal work with Christmas approaching is also a good idea.
It can be difficult when people know you're having an interview and then not getting the job, but your parents should know that this is just the working world. They will be disappointed for you, particularly if it's something you really wanted, but they shouldn't be disappointed in you, and I'm sure they're not.
Best wishes. Hope you get something you like soon.