If you don't consider any punishment the responsibility of a criminal, then I think you're using a different definition of 'responsible' than most people, and this might actually be a semantic argument rather than anything meaningful.
The criminal is only responsible for breaking the law, the only thing he had control over before he was caught (assuming he was caught for the sake of argument). We as society are responsible for dealing out the punishment.
How could the criminal be responsible for the punishment when he is not the one inflicting it on him/herself.
edit: To make my argument slightly easier to understand I'm going to give an extreme example
Let's say it's illegal to be a certain religion. Is it the insert religion here person's responsibility that he is punished and sent to a death camp?
As it turns out, responsibility for statutory laws is only transitive when applied to a party to the statute (e.g. a lawmaker or the enforcer).
A thief is responsible for restitution because depriving someone of their property is violation of natural law. A party who breaks a contract is responsible for fulfilling the terms they agreed to, because they made that agreement.
A thief, or a party who breaks a contract, is not responsible for a _statutory law_ enforced against them (unless they are a law maker or the law enforcer).
The creators and enforcers of the statue are responsible for creating it and enforcing it. They are responsible for its outcome, whether that is a dead murderer or a dead baby.