Translation:I really like to eat Shanghai cuisine.
I think that's a bit harsh. I'm a native English speaker with a reasonable command of the English language, and the translation sounds acceptable to me. Granted, I don't think it's common to say that, and it could very well not be acceptable. However, I think given the context, you could have formulated your response a bit more diplomatically. I'm running this by other native speakers to see what they think. Cuisine is an abstraction of food after all, so you are implying that you are eating Shanghai food, which is perfectly fine.
My explanation is that Shanghai is both noun and adjective. Japan for example is a noun, and it's accompanying adjective is Japanese. Shanghai is simply one of the many exceptions in English grammar. Other examples: London cuisine, Viennese cuisine, New York cuisine, Maltese cuisine. My usage of English grammar is intuitive, so sorry if I missed a technicality here or there, but I think I am getting my point across.
For the sake of proper English, please add different versions of "correct": one that sounds correct to Chinese natives speaking English, and another one (or two) that are correct to native English speakers. Thanks! I really don't like having to make someone "wrong" here, but there are ways of speaking in English that may (sort-of) pass muster on the written page, but would sound awfully awkward if you were to actually speak like that . . . My five cents-worth, as usual . . .