The centre half barged Leicester striker Jamie Vardy to earn a second yellow card after 62 minutes, incurring the wrath of his manager who is under intense pressure after Newcastle's eighth defeat in a row left them in danger of relegation.
"I thought he'd done that on purpose, it looks like he did," Carver told reporters, suggesting Williamson may have been trying to avoid playing in important matches at the end of the season.
"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?
"I thought he meant it," Carver added. "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," said Carver.
Fellow Newcastle defender Daryl Janmaat was also dismissed in stoppage time after another abject performance by the north-east club who have fallen to 15th in the table, two points clear of the relegation zone with three games left.
Carver, handed the manager's job until the end of the season after Alan Pardew left for Crystal Palace in January, was asked to rate his team's display.
"On a scale of one to 10 it is a minus 10," he said. "I asked if everyone understood their roles and responsibilities. I can't go and mark men on the pitch myself.
"If we're not willing to compete, get your head on to the ball and risk getting an injury, you won't get anywhere."
(Reporting by Ed Osmond, editing by Tony Jimenez)
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