The 31-year-old was given a second yellow card when he bundled Foxes striker Jamie Vardy into a cameraman during an off-field tussle.
"I thought he'd done that on purpose - it looks like he did," Carver said.
"The ball was off the pitch - he had no need to make the challenge. He will miss two games. Is it an easy way out?"
Out of sorts Newcastle have been dragged back into the relegation battle in recent weeks and Williamson's reckless red added to Carver's fury.
"I thought he meant it," The Magpies chief said. "When the ball went on to that left-hand side my first reaction was don't do it. He did it. Vardy was off the pitch, Willo was off the pitch, the ball was off the pitch.
"There was no need to do it and I'm not accepting that.
"I told him that to his face. I don't want to go into his reaction."
Carver was in an angry mood at the final whistle and he will have an "open discussion" with his players on Monday.
He added: "There might have been players who didn't try - maybe they don't think they'll get a new contract or be here next year. But they're getting paid and should try."
