'Low key' means that most of the subject matter and background is of dark values, and the lighting leaves large areas in shadow (but not necessarily devoid of detail).
Your attempts don't reflect an understanding of this. Perhaps your teacher doesn't understand what 'low key' actually means. (This would not surprise me.)
Again, note how most of the values are darkish without being actually underexposed. Most of the values are mid-tones and darker.
Here's one that is a bit odd, a portrait of James Cagney that has some elements of low key (namely the shadows enveloping his eyes), so it really isn't exactly low key: