The civil code Art. 751 simply says "A person who has injured the person, liberty or fame of another or has inflicted any mental anguish to another person shall be liable to make compensation for damages arising therefrom". The Criminal Code is more details about punishable offenses, in Art. 307-312. Generally, those laws require alleging facts, which you seem to not have done. However Art. 311 specifically addresses insult: "A person who publicly insults another shall be punished by imprisonment or imprisonment without prison labor for not more than one year or by a fine not exceeding two million won". Unlike the provisions regarding alleging facts, insults have no truth value so there is no defense "it's true and we said this in the public interest" (which is how to get out of a defamation charge in Korea). So it hinges on whether the insult is deemed to be public.
You have to get a Korean attorney who knows the specifics of Korean interpretation, but "public" does not necessarily mean "out there for anyone to see", it can simply mean "anyone at all other than the target of the insult". The usual common law construction of defamation includes communicating the defamatory statement to one other person. Insofar as Korean vigorously prosecutes for defamation, contacting an attorney is a good idea. This article on insult under Korean law suggests that there was a case involving dirty looks (though, in "clear public") deemed to be insulting. The author notes that
This crime requires the insult to be made in public. So, insulting
another person 1:1 is normally okay.
which suggests that Korea follows the common law understanding of "public", namely "to more than one person".