Plenty little supermarkets on just about every main street and the local supermarket (mercadona) is at the end of the campsite on the other side of the railway line. Im sure the receptionist on the campsite will be able to direct you.
I have been to LA SIESTA 2 times and there is a small mini market on the site near the pool but be aware its not cheap in fact its a rip off, stick to the side streets better priced, hope this helps you have fun.