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.
Media playback is not supported on this device
"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.

Euan Walker also let a yacht float out into the North Sea.
He pleaded guilty to wilful fire-raising, wilful fire-raising to danger of life, and reckless behaviour between 16 and 20 March in Musselburgh.
The 29-year-old was jailed for 20 months when he appeared for sentence at Edinburgh Sheriff Court.
The court heard the most serious incident happened in a car park in  Musselburgh's Mall Avenue.
Damien Witowski returned to his Fiat Camper van at about 20:00 on 20 March and went to sleep.
At about 00:05, another motorist driving past saw the van on fire and phoned the fire service. The blaze was extinguished and it was found that Mr Witowski "had actually slept throughout the incident".
Defence advocate, Lily Prais, told Sheriff Fiona Tait her client had turned to alcohol and drugs after separating from his girlfriend.
He had struggled to come to terms with his behaviour, she said, which was entirely out of character.
He had shown genuine remorse and had been completely unaware there had been anyone in the camper van.
Walker, she said, had never been in trouble before and was now living with his family in Edinburgh, who were very supportive.
Sheriff Tait told Walker that given the nature of the charges and, in particular the charge involving the camper van in which Mr Witowski had "fortunately escaped", a custodial sentence was inevitable.

Raiders broke into the house in Old Glamis Road between 18:55 and 19:35 on Tuesday.
A full list of the items of jewellery stolen and details of the foreign currency have not yet been released by police.
Officers have asked anyone who was in the area at the time to come forward.
Captain Ashley Williams has challenged Swansea City to maintain their winning form following back-to-back wins in the Premier League.
[NEXT_CONCEPT]
A man has been jailed for setting fire to six cars in East Lothian, including a camper van in which a man was sleeping.
[NEXT_CONCEPT]
Police are appealing for information after a safe containing foreign currency and jewellery was stolen from a house in Dundee.