Swansea are four points clear of the relegation zone after a much-needed 2-1 win at Everton.
The Swans had beaten Watford earlier in the week and Williams wants the team to continue the momentum.
"The main thing is we build on it and that was my message before the game," Williams said.
"We want to put a run together now and pick up as many points as we can to put a bit of distance between ourselves and the drop zone.
"Every team has a little run, whether it's a good one or a bad one, throughout the season.
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"We'll try and make it our turn to have a good one now."
New head coach Francesco Guidolin's first game in charge saw Swansea secure a first ever league win over Everton and two successive wins for the first time this season.
Wales defender Williams has been impressed by the Italian, who previously coached Udinese and Monaco.
"He's lifted the place a bit and also tried to implement some of his own ideas into the team in the week," Williams added.
"He wants us to play our own game with a few little tweaks and ideas that he thinks will help us.
"I look forward to working with him and all the lads have been impressed with his first week and the way he goes about work and what he's asking of us.
"It looks good at the minute. It's been a good week for us and now we can settle down again, collect our thoughts and go again."
Swansea's next Premier League game on Tuesday, 2 February will be away to the side immediately above them in the table, West Bromwich Albion.
Captain Ashley Williams has challenged Swansea City to maintain their winning form following back-to-back wins in the Premier League.