The OP has made an observation, and wants to communicate it through a pithy adage for ease of memetic transfer. I argue that is observation and his pithy adage are reversed forms of each other, and would only be functional if the original statement was communitative in the mathematical sense.
His observation, as far as I can understand, is simply that where you find evil, the perpetrater believes in their own heart to be good, and furthermore believes that the evil they are doing to be good as well. Now, this has been argued to not be universally true, but I think most people can agree that it is at least sometimes true, and perhaps even often, frequently, or approaching in the direction of always true. Arguments can be made regarding the position of how often it is true, but for the moment, this is the sentiment that the OP wants to encode into a pithy catchphrase.
In order to maximize ease of memetic transfer, the OP wishes to hijack the form of an already successful meme, and insert his variables into the slots of the phrase. The problem is that the meme he wants to change works in the other direction... his observation is that where you find X, the source is Y. The meme is that where the source is Y, you find X. In fact, the precice wording of the meme is that ONLY when the source is Y do you find X, but most people understand that this is an exaggeration. What's not an exaggeration (as most people read it) is that when you find Y, then X necessarily follows. "When good men do nothing, then evil is always allowed to exist." (evil might also exist if good men do things that are stupid or ineffective, but this is less pithy and we can allow this while still accepting the jist of the main statement)
But the OP's observation does not, and cannot work that way. There are far, far, far too many counterexamples. It is perfectly possible to believe you are good, AND TO BE CORRECT. It is possible to try to do good, AND TO SUCCEED. Furthermore, it is arguably possible to FALSELY believe that you are good, and yet fail to do evil. It is even arguably possible to FALSELY believe you are fighting evil, and yet not perpetrate evil in the process. (It is furthermore possible for men to not believe they are good, and to commit evil, but this only counters the strong form of the statement, which most people are willing to let slide when it comes to pithy adages).
So no, the OP's adage does not effectively communicate his idea, because it goes in the wrong direction. A -> B does not imply B -> A.
The next question is of course whether the observation that "evil deeds are often done by people who think they are good trying to fight what they believe to be evil" is sufficiently accurate for a large enough subset of evil events to be worth of an adage, and what would the appropriate reaction be to the hypothetical correctly formulated adage. The correct response to the original adage is to spur "good men" to get off their butts and actually do something about evil. The correct response to the OP's observations would be... to do what? Another poster earlier in the thread suggested that the correct response would be to sit down and watch TV, in order to prevent oneself from doing evil when they believe themselves to be good. This seems... counterproductive, and not a good response, and yet it flows naturally from the observation.
I suspect the OP would prefer the proper response to his hypothetical adage be that individuals perform deep introspection to really attempt to determine whether or not they are actually good, and their targets actually evil, before acting. Of course, such deep introspection is inherantly mired in all kinds of complications which actively work against being compacted into a pithy adage. Defining what is good is HARD. Defining what is evil is HARD. I mean, sure, it's easy to make broad categorizations, but it seems that making broad categorizations is what leads people to think they are good and their opponents evil in the first place!
So....... I don't think this idea can, or SHOULD be made into a pithy adage.
Surely it is as ridiculous to consider sqrt(-1) "imaginary" because you can't use it to count pieces of chalk as to consider the number 200 imaginary because by itself it cannot express the location of one point with reference to another. -Isaac Asimov