The Swans defeated the Canaries 3-0 at the Liberty Stadium to move up to 13th position on the Premier League table which has them seven points clear of 18th-placed Cardiff City.
With six matches left to play, Williams has urged Swansea forward as they look to preserve their status as a top flight club.
"What we don't want to focus on is getting to 37 or 38 points and then stopping," Williams told the South Wales Evening Post.
"We're trying not to lose again this season, to win as many as we can and to just keep going. It's in our hands.
"We're not saying: 'Let's go for two more wins'. Forget that. We've got six games left so why can't we try to win them all? If we can't win them, let's not lose. That's the way we're looking at it.
"It's a bit bullish to say that after we've just drawn one game and won one game, but that's the way we feel.
"We've got to set our standards high and get back to where we have been in the last two years. We want to finish the season strong and take the momentum into next season."
Swansea next meet 14th-placed Hull City at the KC stadium on Saturday.
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