That's not a valid criticism of the sales tax. In Florida, for example, supermarket food purchases are not taxed. Nor are residential rents (until they get into the "luxury" level), nor medical services. In principle, and in practice, the poor can live their lives relatively unaffected by a well-crafted sales tax.
In North Carolina, we have a special Food Tax added to all food purchases. Most states have Soft Drink taxes, Fuel taxes, sugar taxes, ...