I think this has been hinted at;
TV Spot;
Punisher - "Red, you're angry, aren't you? I can see it on you, it's all over you. You hate yourself. It's eating you up because you ain't done a damn thing about it. I don't think you came here for my help. I think you want my permission, Red. You wanna get your hands on someone, you wanna hurt them. Maybe you're a little bit scared about what that means. But it's gonna keep eating, and eating, and eating, cause you know they're breathing the same air that you're breathing."
And in the first episode;
Matt - "As you know, I've stood in this court may times. Delivered summations, called witnesses, and defended the innocent to the best of my ability. Though as I sit here, on the other side of the court, it occurs to me that justice will not be served today...*omitting spoilers*... but in the absence of justice, the court can punish this man. And I urge you to do so, to the fullest extent the law allows. Because that punishment, that is the closest any of us will ever get to justice."
Now, I understand that in the second example he is talking about punishment by the law and from the courts, ie. the imprisonment of criminals and not the killing of criminals. But, I think it shows a shift in his mindset that he now believes the law will never achieve the justice that he sees these criminals deserve. He know views these people through the lens of "punishment", rather than "justice". By it's very definition, "punishment" is not tied into law in the same way that "justice" is. In Matt's mind, the law and "justice" now appear to be secondary to inflicting "punishment". Today, the punishment of imprisonment is the closest he thinks we can get to justice, maybe tomorrow it's the punishment of death.