"Confidence is slowly coming back and you can only get confidence by performing well," Williams told reporters.
"You can see the guys are trying to play out of tight situations, which they maybe wouldn't have done earlier this season."
Williams also heaped praise on the Swansea defenders.
"We kept another clean sheet, which is really pleasing, as well as another point towards where we want to be," Williams said.
"I think it was our best defensive display of the season. We had to defend a lot of crosses and, as a unit, the desire and heart was there for everyone to see.
Swansea, who are fourth from bottom in the table after 19 games, travel to sixth-placed Manchester United on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
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