Going by canon sources, only, we don't have much information on how Itachi killed the clan. I'll exclude CNN's merchandising from my evaluation of his character, and assume he didn't have a whole lot of time for torture in the middle of attempting to murder a whole clan in a single night.
I don't think Itachi ever really sought forgiveness for his actions. Not to say that I don't think he felt any guilt or questions about it, but that I think he saw himself as simply a cog in the wheels of a much larger machine. He had faith that the ninja world would become a better place, and was content to allow his actions, evil good or otherwise, to be a contributing factor in that outcome. I think, in many ways, Itachi believed that the entirety of the Uchiha was not fit for that world, including himself. Itachi saw the Uchiha's way of thinking as being entirely contradictory to any kind of enduring peace, and his isolation from the village was as much self-imposed as it was a consequence of his actions. Itachi saw himself and the Uchiha as part of a past best left to the past, and thus, likely saw himself as the arbiter of a judgment that would play out over time... either all at once, or bit by bit over generations.
Basically, I would say that Itachi saw the Uchiha as having no future, and was more than willing to accept his own removal from a better future. The only person he couldn't destroy the future of, so easily, was Sasuke, and he desperately hoped Sasuke would find a way out of the same path of thinking that the Uchiha were in. As such, he likely felt a great amount of despair, but never really would have sought forgiveness in the same sense we typically think of it.
