Wales found themselves 17-9 down to a spirited Canadian side in Nantes yesterday before the introduction of Stephen Jones and Gareth Thomas from the bench changed the game.
Williams scored twice as Wales ran in five tries in the last 30 minutes to open their campaign with a 42-17 win.
Next Saturday's pivotal clash with the Wallabies in Cardiff is set to determine who finishes top of Pool B.
And Williams said: "We certainly know we can't start as we did today against Australia or the game will be over at half-time.
"There are still a lot of areas where we are immature, things like discipline in ridiculous areas.
"We are losing 30 or 40 yards because we are giving penalties away in scoring areas. "We certainly know we can play well in patches but against the best teams in the world that is not enough.
"There was good variety in the way we played today and we showed in patches what we can do."
The victory allowed Williams to joke about a major blunder midway through the second half when he fumbled the ball after making a 40-metre break and a try a virtual certainty.
It was an embarrassing moment he soon made up for with two tries of his own, adding to scores from Sonny Parker, Alun-Wyn Jones and Colin Charvis.
"I knew Alfie was on my shoulder and I was in two minds whether to pass or kick. And the rest is history," he smiled.
"Just afterwards someone clattered me in the head and I probably deserved that!
"That could very easily have finished me - but I was determined to do well and at least I can laugh about it now because we won.
"It was a difficult game and the Canadians certainly surprised us."
Wales head coach Gareth Jenkins hailed the impact made by Jones and Thomas after they came off the bench to turn the game.
"We were disappointed in our performance at half-time," said Jenkins.
"Canada had a part to play in that and you have to give them credit for putting the pressure on us."