Williams provided the spark in an outstanding Welsh performance that he believes will silence the critics.
'The team has taken a lot of stick and been accused of not showing enough passion or heart but I think we proved them wrong against New Zealand,' he said.
'Coming off the field there was a lot of disappointment because we knew we could have won the game, but there were also a lot of smiles because we knew we had put in a good performance.
'For the boys to feel the same next week we are going to have to perform just as well, if not better, in what is an even bigger game.'
Skipper Colin Charvis added: 'Nobody really gives us a chance against England and there are going to be voices in our heads that raise doubts but we've got to focus on the voices that urge to give a good performance.
'England are ranked No 1 in the world and there's won't be much money on us but we have got to into the game with a positive attitude,' he said about next weekend's quarter-final against the English.
'We've got to be strong and look forward to that game just as we did against New Zealand.
'We came to the World Cup with the attitude that if we keep improving from game to game then we can compete with the best in the world and I feel that we have gone up a few rungs in the ladder.
'But we know we are going to have takes another few steps up to beat England.'
The biggest dilemma facing Hansen ahead of that game is selection for the Brisbane clash following several outstanding performances - not least Williams and Jonathan Thomas.
'I have got a few selection headaches now but that was one of our goals for this World Cup,'
'The minimum was to reach the quarter-final and we've done that but we also wanted to develop a few of these younger players for future competitions.
'Shane played very well while Jonathan proved not only to everyone else but to himself that he could be a very big player for Wales in the future if he repeats that performance whenever called on.'
Thomas indeed looks to be a young man who has a big future ahead of him having taken on the All Blacks single handedly. after making his debut against Australia in the summer.
'When I got the nod that I was playing I was just grateful for the opportunity to play with the eyes of the world watching as I have had to bide my time with so many senior players in the squad,' he said.
'The atmosphere out there was amazing and it really lifted the players when they heard the crowd chanting for Wales. It was a special moment.
'This gives us a real buzz now for the England game. We've been kicked in the teeth over the last 12 months but a performance like that gives us all a lot of heart
'The team spirit has always been good in the squad. Even during the low times everyone has stuck together. We're still a pretty young side but we will learn so much from this game.'