I want to say that envy and schadenfreude are essentially irrational, in that these emotions involve implicit normative misjudgments. Envy involves responding to something good (for another person) as though it were bad, and schadenfreude involves responding to something bad as thought it were good. In general, I hold, emotions involve implicit judgments, and can be rationally assessed according to whether those judgments are themselves rationally warranted. But might this approach be used, by moral responsibility skeptics, to argue that blame is never warranted?
Someone might suggest that the reactive emotions associated with blame (resentment, guilt/shame, etc.) involve an implicit claim to the effect that the target deserves to be punished, or that it would be a good thing if this were to occur. But many people are skeptical of such retributivist claims. We may instead think that for a person to suffer is never good in itself (even if the person in question is bad). Does this then commit us to the view that people are never blameworthy?
Well, only if we accept their initial suggestion about what implicit judgment is contained in the emotion of blame. And I don't see any reason to accept that. Of course, many folk are retributivists, and so would be happy to see the people they consider blameworthy suffer. But this seems a merely contingent connection. As I see things, moral emotions like resentment or moral indignation merely involve, in the first instance, a kind of negative judgment or moral disapproval. Roughly, as per Nomy Arpaly's account, to hold someone blameworthy for an action is to hold that they manifested a "deficiency of good will" in so acting. It is this normative judgment that is implicit in the negative moral emotions, or so it seems to me, not any stronger claim to the effect that it would be a good thing for this bad person to suffer. How we should respond to the identified deficiency is a strictly further question.
It's important to distinguish here between blame and outward expressions of blame (e.g. vocally berating the person). To express blame is an action -- a form of punishment -- that may be advisable or not as the practical reasons dictate. All else equal, we may think there is a pro tanto reason not to so act, namely that it's unpleasant for the recipient. We shouldn't want people to suffer unpleasantness (unless it's instrumental to some greater good, e.g. deterring future wrongdoing, that can outweigh this consideration). This is the standard anti-retributivist point. But even if expressing blame is inadvisable, it doesn't follow that blame itself is unwarranted. (Just as one may be warranted in feeling fear, though it may be inadvisable to scream or otherwise express this emotion if that may trigger panic in others.)
This is the crucial point. While expressing one's moral disapproval may be an act of 'punishment', and (pro tanto) inadvisable for that reason, the same simply isn't true of feeling moral disapproval in the first place. Emotions aren't actions, and so a fortiori aren't acts of punishment. They may be practically fortunate or unfortunate, but those aren't the kinds of considerations that determine whether a given emotion is rationally warranted (just as practical considerations aren't relevant to rational belief). Rather, what matters is whether the implicit judgment in the emotion is warranted. So it all comes down to the question whether the moral emotions involve implicitly judging punishment to be desirable. Do they? (How, exactly, could we go about settling this question one way or another?)
P.S. For a somewhat different take on what blame consists in (which I'm also sympathetic to), see my old discussion of Scanlon's view.