The 30-22 reverse was Wales third of the campaign so far and Steve Hansen's men must now pull something out of the bag against either Ireland or France to avoid a whitewash.
But Williams, who was handed the captaincy for the Murrayfield clash, has urged the critics to lay-off the squad as they learn their lessons.
"I still believe that this side can be something special in the future as long as people stop knocking us down," said flanker Williams.
"It is still a very young side and many of the boys are playing in their first Six Nations campaign. A lot of them had never played at Murrayfield before and it is not an easy place to come and win.
"When you look at Scotland they have gots loads of experience throughout the side and some class players.
"We just need time to develop and to gel.
"If you took the first 20 minutes out of the equasion we were easily equal to Scotland and dominated the second-half.
"It was frustrating that we didn't make better use of the ball and score earlier but there were plenty of reasons to be optimistic in that second half.
"Leading the team out as captain was an awesome experience but it was just bitterly disappointing that we lost."
Meanwhile wing Gareth Thomas admitted a third defeat has upped the stakes ahead of their remaining games of the championship.
He said: "Ireland at home and France in Paris are very big games for us now and we will have our backs against the wall.
"But I think some of the boys did play well against Scotland, especially Rhys Williams, and we will just have to sit down and watch the video to see where we want wrong."
Stephen Jones said:
"When you play for your country everyone wants you to do well and win. If you don't, it comes back on to the team and from our point of view hat's fair enough.
"But in reality, what we are talking about here is a very young side.
"The fact that we wasted so many chances is good . . . and it's not good. We must have been doing something right if we created so many chances.
"But it was also a bad thing because we were so many points behind and chasing the game.
"We didn't really show patience in our game and that is a big learning curve we have to heed. "