A wrong is unredressed when retribution overtakes its redresser.
may best be understood with the preceding sentence:
I must not only punish but punish with impunity.
The narrator Montresor feels wronged by Fortunato and wishes redress for those wrongs done to him, i.e., he wishes compensation. Which in Poe's tale takes the form of Montresor killing Fortunato. But Montresor wants to get away with the murder -- he won't feel things are set right if he is punished in turn for the punishment he inflicts on his victim.
When Montresor says
It is equally unredressed when the avenger fails to make himself felt
as such to him who has done the wrong.
he means that he (as the avenger) won't feel things are set right if the victim doesn't realize who's doing the punishing. It's not enough for Montresor to kill Fortunato; Fortunato must understand that it is Montresor who is killing him.