This "on the slide" thing is massively overplayed.
It's true that our form had been patchy in the November and December before he left, but that was after 18 months of mostly outstanding results and entertainment. The weakness of our defence, and perhaps more specifically our defenders (Baldwin, Rawlinson, Cameron) at League Two level was beginning to show in the lead up to Christmas and continued to be evident after Williams left, but Luke's "bad run" wasn't actually that bad at all. It was probably accentuated by the excellence of what had gone previously, and some disgruntlement that he had so readily taken the Swansea job, but that's football.