Theft from bags / handbags at the market is a common occurence I'm afraid. Not just at the Los Narejos one but any market. Here in Almoradi where we live it is the norm for the handbag thieves to be on the prowl.
My advice - wear a proper money belt that you can tuck inside your trousers or a bum bag with the pouch round the front.
If you HAVE to take a handbag then wear it over your shoulder - crossed over your body - so that it sit on your tum. And keep one hand on it at all times!
Times are hard in Spain so anyone who looks prosperous is a sitting duck I'm afraid.