As the argument goes, if everything in the universe is determined, then we are determined too. It seems something everyone can accept, but for some this destroys any possibility of having free will. Thus, the argument goes, any form of retributive punishment is left over from a prescientific understanding of action.
I'm personally a compatibilist, but for the sake of argument, let's assume there is no such thing as moral responsibility because of this determinism. If people have no moral control, then what good does it do to punish them?
I can think of two reasons in which retributive punishment would be desired. First: if our psychology worked through negative feedback; that punishment was an important means to be aware of the wrongness of such an action. Perhaps retributive punishment, may be a means to show the seriousness and the unacceptability of such behaviours. Second: if such punishments were a means to deter crime; that as agents that can predict future states and desirability of outcomes, the notion of retributive punishment was itself a preventative measure.
This is not to say that because we can justify retributive punishment that any form of retributive punishment is acceptable, or that one is justified in wanting harsher treatment for individuals - after all, they're still humans and torturing someone who has committed a crime for example won't uncommit the crime. But that even if we have no moral responsibility in the way that an incompatabilist would describe does it mean that therefore retributive punishment is never warranted.