"We've got a stack of talent in our dressing room. Nobody was questioning our ability as a side after the Ireland game, but perhaps a few harsh truths will come out of this performance.
"We haven't performed to our capabilities and we know we should be playing a lot better. It is difficult to put a finger on what went wrong. This is a bit of a wake up call for us all."
Williams pointed to a combination of basic error by Wales and a Scotland team that had worked hard at unlocking the gameplan of their opponents as the reason for the away side's shortcomings on Saturday.
"We just couldn't keep the ball, and when we did get our hands on it we didn't use it wisely," he continued. "They did their homework on us and played well. We won plenty of ball against one of the best packs in the world last week, but we couldn't do the same this time round.
"We felt quite fresh, but we played into their hands, we didn't take the sting out of them. We are absolutely gutted. We weren't happy last weekend when we lost, even though we played quite well, but this is far worse a feeling."
Having lost their opening two matches in the 2007 RBS Six Nations campaign any thoughts of winning the Championship have gone for Wales. Now it is a question of regaining some pride; starting with a trip to Paris in two weeks time to meet the French.
"France are going to be strong favourites," concluded Williams. "However, we've been in this position before going to Paris."