Wales can take heart from their impressive performances in victories over Ireland, France, Italy and Scotland as they look to the Junior World Championship this summer - a competition in which they finished third last year.
But Williams believes Wales, who received eight yellow cards across the tournament, must work on their discipline ahead of the summer's trip to France.
"It meant a lot to the boys to get the Grand Slam and make history and it felt like failure, it was gutting," he said.
"The boys just need to pick their heads up, learn from it and build to the World Cup.
"Discipline is something that we do need to work on with eight yellow cards in the tournament but to be fair to England they punished us.
"There are plenty of positives, we came in looking to build for the World Cup and we've achieved a lot and when we come back into training we have to learn from this game and take it into the World Cup.
"The boys have grown a lot in this campaign, the mood in the camp has been very good and everyone has been backing each other up."