"Tea, not coffee!"
Translation:Herbata, nie kawa!
The only case which changes when negated is when the verb needs Accusative. And indeed, if you wrote "I drink tea, I do not drink coffee!" that would be "Piję herbatę, nie piję kawy" and Genitive would be used. But here, the thing negated is not any verb, but just the noun, so it stays. It's a relatively rare situation throughout this course.
Herbata is nominative case- the form of noun that it takes when it is a subject of a sentence - like tea is hot - herbata jest gorąca. It is also "dictionary form". which is the one you see at dictionaries and pick when there are pictures in duolingo.
herbatę is accusative case, -the form of noun that it often takes when it is a object of a sentence. Poproszę herbatę means literally I will ask for tea