The home side were on top for much of the game, with Wilfried Bony and Williams himself guilty of missing presentable opportunities in the first half.
The result leaves the tie wide open, and Swansea will travel to Naples for the second leg next week knowing that a win or a score draw will see them through to the next round.
And despite the sense of disappointment, the Swansea captain insisted there were a lot of positives to take from a draw against a side who came within a whisker of qualifying for the knockout stages of the UEFA Champions League.
"It says a lot to say we are disappointed with a 0-0 against Napoli," he told ITV.
"We are really pleased with the way we played.
"We emphasised the message to get on the front foot. It does not matter who comes here, we want to do that.
"It will be a tough game in Napoli - we are under no illusions.
"We can take a lot of heart from tonight."
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