expression, noun
disapproving look; disgusted eyes; nasty glance
Refers to a facial expression showing disapproval, disgust, or contempt. Often used in the pattern 嫌な目で見られる (to be looked at with disapproving eyes).
彼は私を嫌な目で見た。
He gave me a nasty look.
周りの人から嫌な目で見られるのがつらい。
It's hard to be looked at with disapproving eyes by people around me.
expression, noun
unpleasant experience
Used in the set phrase 嫌な目に遭う (to have an unpleasant experience, to go through something bad). The noun 嫌な目 itself is not freely used outside this construction.
See also: 目に遭う
旅行先で嫌な目に遭った。
I had an unpleasant experience at my travel destination.
The verb phrase meaning 'to experience (something unpleasant)'; 嫌な目 is the noun part that pairs with it.
A compound of 嫌な (unpleasant, disagreeable) and 目 (eye). The second sense is an idiomatic extension where 目 stands for 'experience'.