14 points from Leigh Halfpenny helped Wales claim their third consecutive RBS 6 Nations win on the bounce but Williams maintained the victory was built on the side's defence.
Wales conceded just three points - one of four Owen Farrell penalties for England - when fly-half Rhys Priestland was in the sin-bin in the second half and Williams said: "It is quite unbelievable really, I don't know what to say.
"Our defence was superb, we stuck in there and managed to get the win. We tried to keep hold of the ball after Rhys Priestland's yellow card. England put us under pressure, but we soaked it up until it was time for him to come back on."
And Williams' joy was certainly shared by Wales boss Warren Gatland. While admitting his youthful side stuttered in front of the partisan Twickenham crowd the Kiwi was only in the mood to hand out praise.
"I'm very proud," he said. "It was tough and we said that it would be before the game. We had a chance to create some history winning the Triple Crown at Twickenham.
"The guys showed tremendous character hanging in there. They were young boys who froze a little bit on the big occasion.
"This will be Rhys Priestland's biggest learning curve.
"I thought England played really well. They made their tackles. It was a good, tough test match. "There was nothing in it.
"But the turning point was when we were down to ten men. It was 3-3 in that time. We kept hold of the ball and played really well.
"England didn't make it easy for us. We scrummaged well. We probably had just a little bit more fire power than they did but there wasn't much in it.
"This team could be outstanding. We've got a bit of depth right now and you've to be excited about Welsh rugby at the moment."