There is a good selection of local Cavtat supermarkets which are accessible from most villas and apartments and which should provide all you need day to day!
The little shop in the old town in Cavtat is usually open until 9pm on Sunday
Pemo Supermarket (medium sized) – in Mocici ( halfway from airport to Cavtat ) Monday – Sunday 7am – 9pm
Pemo Supermarket (medium sized) – in Cavtat Monday – Saturday 7am – 9pm, Sunday 7am – 2pm
Tommy – in Obod (2 km from Cavtat) Monday – Saturday 7am – 9pm, Sunday 7am – 9pm