I know this comment is 3 months old, but maybe it will help someone else who happens to have the same query.
So, "It does not effect me" is not correct English. This has to do with the difference between effect vs affect. Usually, effect is used as a noun and affect is used as a verb. So for this to be grammatically correct in English, you'd say "It does not affect me" because here you're using the word as a verb. If you don't want to use it as a verb, then you'd say "It does not have an effect on me". See the difference? You can look up the difference between effect vs affect as others explain is far better.
Now as to whether Duo accepts "It does not affect me", I can't say.
Hi Dbeeva, you can use it in any occasion when something "touches" you (physically or psychologically) and it has no effect on you. In my previous post, I wrote some examples: you walk outside while there is a cold strong wind, you can say "De wind doet me niks omdat ik goed gekleed ben" (I am learning English, however I'll try to translate it like this:) "The wind does not have effect on me because I am dressed well" Or: "Zijn beledigingen doen me niks" "His insults don't have effect (meaning:"don't hurt") on me. Best wishes, Lu.