Hazard was sent off by referee Chris Foy after he appeared to try and kick the ball from underneath the tracksuited youth who was laid prone on the ground.
"Demba Ba told me the ballboy held on to it," Williams said. "I saw him kick him in the rib and you can't do that to a young boy."
A 0-0 draw at the Liberty Stadium ensured Swansea set up a final against Bradford City following a 2-0 aggregate win and Williams was delighted.
He continued: "At times tonight it was like a bar fight especially when they were pushing on.
"The team defended brilliantly. That's what we worked on. We wanted to bring them back here and score a goal and keep a clean sheet. We didn't score but we kept a clean sheet."
Midfielder Leon Britton was equally ecstatic, adding: "It's unbelievable tonight. To do it over two legs against a team like Chelsea - tonight we made history.
"The club has come on leaps and bounds over the past 10 years."