Pascal explained it really well.
In Korea, when you are not good at something, you can also use the expression "(~에) 서투르다, " the same as "잘 못해요." 서투르다 means to be unskilled or unfamiliar.
Examples:
한국어 잘 못해요 = 한국말 서툴러요: I'm not good at Korean.
한국어 아직 잘 못해요 = 한국말 아직 서툴러요: I'm not good at Korean yet.
한국어 아직 많이 잘 못해요 = 한국말 아직 많이 서툴러요: I'm not very good yet.
운전 잘 못해요 = 운전 서툴러요: I'm not good at driving.
So, in your situation, I would say 한국말이 아직 많이 서툴러요, 그래서 파스칼님의 설명이 마음에 들어요.
As Pascal wrote, in many situations you cannot go wrong with saying "마음에 들어요 when you like something. 마음에 들다 means "it comes into my heart; therefore, I like it," and also sounds more mature than 좋아해요.
But, when you simply like something such as ice cream and Korean food, 좋아해요 sounds better. i.e. 아이스크림 좋아해요! :)