He could make little impact as the Scots began the match in rampant fashion, with prop Bruce Douglas and number eight Simon Taylor touching down to help rack up a 17-3 lead after just 22 minutes.
But Wales fought back and dominated large periods of the second half, spending much of that time camped in Scottish territory and winning several penalties in succession.
They trailed 23-10 and each time Williams ordered fly-half Stephen Jones to kick the penalty for field position rather than take a shot at goal, spurning the opportunity to eat away at Scotland's hefty lead.
"We had a lot of momentum and there was not too long to go. We needed two tries so we thought it would be better to kick for the corner and try and sneak a try," said Williams, Wales' third skipper in three games during this year's RBS 6 Nations championship.
"It didn't come off and maybe with the benefit of hindsight we should have kicked the goals but I don't think it would have made too much difference."