He talked about Cold Harbor for several pages in his memoirs before the "regret" part. All the maneuvers that went on during the campaign were to get into a better tactical position and then attack. And that's what he was planning at Cold Harbor. To again take the offensive. This is the order he sent Meade at 7:00 am on the morning of June 3rd:
"The moment it becomes certain that an assault cannot succeed , suspend the offensive ; but when one does succeed , push it vigorously and if necessary pile in troops at the successful point from wherever they can be taken . I shall go to where you are in the course of an hour."
The regret that he felt was for the loss of life for no measurable gain. But he certainly did talk about the military movements and reasoning leading up to it.