Yes, how dare Alistair not be offended at a traitor get away with this actions. He clearly needs to grow up and become apathetic and non-moral about justice like Loghain and Anora were.
He needs to understand what justice actually is. Butchering people (especially with no regard for their loved ones who would be witnesses to that. Kinda makes Alistair a hypocrite if he's willing to have Anora suffer a sight far worse then he did) and slapping the label of "justice" on it doesn't make it so. I would not call Maric's act towards Katriel justice, nor the act towards the bootlicker nobles that killed Moira, yet those things are called justice by too many people (in-game and out).
Remember the terms of the duel. Two parties fight until the other yields. Technically speaking, we broke that arrangement if we kill him. If justice was to occur and Loghain was to be executed, he should have been imprisoned and sentenced in one go. Or perhaps given the chance to fight as a non-Warden under our authority, with the knowledge he'll die afterwards for his crimes.
I would not call our butchering of Howe in his home justice. For all the crimes he's committed, what we did was still a flagrant violation of the law that should come with repercussions considering we're Wardens (an order that was exiled for rebelling against a king, justified as it was. Even Duncan was unwilling to go against Vaughn despite how he needed to answer for his crimes).
I would be hesitant to call the CE's killing of Vaughan justice as well, but that one I can at least defend because Elves don't get justice to begin with so it's a moot point.
Justice is about more then killing people who wronged you. And Alistair's reasons for killing Loghain are shallow. He focuses more on himself then actual legitimate reasons he could be killed, like the slavery.