The Swans eased their relegation fears over the weekend as they earned a comfortable victory at the Liberty Stadium.
Following a winless run of six matches, Williams is pleased that he and his teammates were able to put in a positive display and claim the points.
"The win was massive, especially with the way we won by scoring three goals and not conceding," he told the South Wales Evening Post.
"It was a complete performance. I don't know how it looked, but I felt we played really well.
"It felt good. We kept the ball well. We didn't have to defend for our lives at the end, with a one-goal lead or anything like that. It's just what we needed."
Swansea continue their Premier League campaign this Saturday when they travel to Hull City.