The Wales international felt his team lacked the desire needed to get a positive result at a raucous Cardiff City Stadium.
"We did not play well, we did not get into our rhythm and we did not pass it well enough," said Williams.
"We weren't solid enough off the ball, and we didn't show enough heart, in my eyes.
"It was bitterly disappointing. I don't think we played well, I don't think we showed enough desire."
And Williams is particularly unhappy that Cardiff's winning goal came from a corner, Steven Caulker getting the better of Chico Flores to head home.
"How many times have I spoken about defending set-pieces?" he added. "It's getting ridiculous now.
"If we can't defend set-pieces we don't deserve to win the game, and we didn't again today.
"We have spoken about it so much, it looked like we had tightened up.
"I don't think they would have scored today if it hadn't come from a set-piece, I don't remember Michel (Vorm) having a save to make.
"(At set-pieces) you've got your man. I know my man, it's me against him, he doesn't score against me. If he does, it's my fault, it's that simple."