For argument's sake, whether or not anyone believes in the death penalty is irrelevant to what happened tonight. Currently, the penalty of capital punishment is a legally available sentence in capital muder cases in some states with Georgia being one of them. Trying to debate the justness of capital punishment itself is, as relates to Troy Davis, a mute (not moot) point.
To the extent that capital punishment is a legal remedy that was pursued and given in Troy Davis' case, the question isn't "should we use the death penalty?" rather it becomes "should we use the death penalty in cases where doubt is present?" I realize that instantiation of "doubt" is rather vague, so let me clarify. By doubt, I'm not referring to cases where the accused has openly admitted guilt completely uncoerced or where there is clear and convincing, substantive evidence (see: Lawrence Brewer) as to the guilt of the accused. By doubt I mean cases including, but not limited to that of Troy Davis, where the bulk of evidence is a reliance on eye-witness testimony and lacking any or all substantial scientific, forensic merit. To be honest, it's a shame that eye-witness testimony is so higly regarded in the USCJ system, because any psychologist worth their bachelor's degree will tell you that eye-witness testimony is so unreliable as to be laughable. Ever play the telephone game in 5th grade? Yeah, now you see what I mean.
That's why it typically takes decades for inmates on death row to be executed. The court makes sure all the defendant's appeals can be exhausted and all the evidence does not leave any reasonable doubt whatsoever that said defendant committed the crime. Only then are they executed.
As I said, I find this particular case saddening because it appears that there were many reasons to doubt that Troy Davis deserved the death penalty.