Strictly speaking, all punishments for crimes are retribution; the court sees the offender as deserving of retribution for breaking the acceptable social conduct. However, as a matter of simple revenge, capital punishment should never be used. A murderer is executed both to prevent further murders and to punish the crime; the killer is killed, an eye for an eye.
Revenge clouds the mind and keeps people from thinking objectively. When a person or society is bent on revenge for a crime, the actual facts and severity of the crime no longer matter; the offender is convicted in the court of public opinion and so due process becomes biased. Think of famous and recent legal cases where the public-at-large is convinced of the offender's guilt; due process is pressured to provide the popular result, not the one that would result from a strictly objective process. This could potentially result in mob action or even bounties to "correct" the court decisions, creating vigilante and mob justice instead of legal justice.
Bear in mind that capital punishment is increasingly unpopular even in cases where there is no sympathy for the offender; the idea of a societally-approved execution process has become about shifting moral and ethical standards, not about actually punishing crime.
In any case, the use of capital punishment as a selective, appropriate response to truly terrible crimes is always under debate. If retribution is meant as revenge, then it is not appropriate; if it is considered as punishment to fit a specific crime, arguments can be made to support retribution.