"Plot" would be the correct word. A "plot" has a specific use, whereas a "parcel" is just an area of land. Refer to these definitions (from Oxford Dictionaries):
2 A quantity or amount of something, especially as dealt with in one
"a parcel of shares"
2.1 A piece of land, especially one considered as part of an estate:
"she decided to divide her property into three parcels and invite sealed
3 A small piece of ground marked out for a purpose such as building or
"a vegetable plot"
I personally would only ever expect to hear "parcel" if there was some sort of transaction (buying or selling land) or transfer (inheritance or donation of land) involved in what was being said.
If you were referring to an especially small piece of land used specifically for growing vegetables, you could also use "allotment." With that usage, ownership isn't implied – rather, you're likely to rent an allotment if you want to grow vegetables but don't have a suitable garden:
A plot of land rented by an individual for growing vegetables or flowers:
"I would advise all residents who have considered renting an allotment
to 'come and have a grow'"
You might also use "zone" if the pieces of land are officially categorised (e.g. by a council or government) for a specific use:
1 An area or stretch of land having a particular characteristic, purpose,
or use, or subject to particular restrictions:
"a 40-km demilitarized zone"
figurative "United are still in the relegation zone"
VERB [WITH OBJECT]
1 Divide into or assign to zones.
1.1 (often as noun zoning) Divide (a town or piece of land) into
areas subject to particular planning restrictions:
"an experimental system of zoning"
1.2 Designate (a specific area) for use or development as a particular
zone in planning:
"the land is zoned for housing"