Seems like you are blending the concepts of punishment and that of revenge. While a criminal, who’s crime has been proved in court should absolutely be punished for the crimes he/she committed according to the corresponding law, the sentences should not be led or even influenced by the feeling of “taking revenge for the victims”, because that’s not what a punishment should be about.
I guess this is one of the main differences between judicial systems and their underlying philosophies in the US and in Europe. While in the US the state can kill / execute some person, because this person has killed another person, that would be unthinkable in Europe, because the state does not have such a “right” and killing / executing a murderer would also be a crime against that person’s life.
European systems are more driven by the idea of “resocialising” criminals, so that they could eventually become acceptable members of society again some day.