The Swans fought back after going two goals down inside 25 minutes, and looked to be heading three points after striker Wilfried Bony put them ahead late in the game.
But Charlie Adam's penalty, controversially awarded by referee Robert Madley for handball against Wayne Routledge, saw both sides leave the Liberty Stadium with a point apiece.
Williams gathered his team-mates into a huddle on the pitch following the final whistle, a move he says was to remind his players of their improved performance despite the result.
"Things haven't been going our way so it would be easy to shy away from it, not want the ball, not play our game and not show some fight," said the central defender.
"We didn't do that, we stuck together and played brilliantly in the second half.
"I just wanted to say to the boys that that's the level we should be at. We have shown what we can do and everyone that we are still united in the squad.
"We have to stay on top and play our game and our tempo throughout 90 minutes. The first half was okay, but the second half was what we want."
Williams admitted he was stunned by the decision to award Stoke the penalty, six minutes into time added on.
"It seemed like none of their players asked for a penalty, maybe one of them was appealing for a corner," he added.
"It was a shock to everyone and I didn't see a handball from Wayne or Leon (Britton). I think both sides were surprised by the decision."