Williamson saw red just after the hour when he collected a second yellow card for a late, knee-high challenge on Leicester’s Jamie Vardy on the touchline just after the hour.
He was followed off the pitch by Daryl Janmaat who was also sent off in injury time during what proved another dismal afternoon for the crisis-hit Magpies.
After eight successive Premier League defeats, Newcastle are nosediving towards relegation and Carver was furious after the final whistle at the King Power Stadium, with Williamson the prime target of his ire.
“I thought he meant it,” Carver said.
“When the ball went onto that left-hand side, my first reaction, five yards before making the tackle was, ‘Don’t do it’ – and 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. I am not accepting that, especially in the situation we are in.”
Asked why Williamson might have done something like that on purpose, Carver said: “I don’t really know. It was just my thought when it happened. I thought he meant that and I have told him so.
“I have actually said this to his face.”
Newcastle fell behind within a minute as resurgent Leicester, fully fired up and determined to maintain their survival charge, stole the ball from the kick-off and Leonardo Ulloa headed from a corner.
Wes Morgan added a second after 17 minutes and an Ulloa penalty put the result beyond doubt early in the second half.
Newcastle were booed off the field by their increasingly angry fans, some of whom held up a banner accusing the team of not trying.
Some of the players were later jeered as “cowards” as they boarded the team bus on their way out of the stadium.
“I can’t disagree with them, Carver added.
“I know some of them went over at full-time and the fans had a go, and more or less said, ‘We don’t want to see you’.
“If I was sitting in the stand with them I would be doing the same thing.
“We are a soft touch. We are a soft touch when the ball comes into the box because we are not prepared to put our heads on it.
“We can talk and talk, but we need to grow up and we need to accept it. The ones that don’t want to grow up and accept it can stay at home.”
Newcastle have been locked on 35 points since February while Leicester were adrift on 19 points and seemingly doomed at the start of April, but now just a point behind them after five wins from six.
“It is in our hands to do something about it,” Carver added.
“We have got to do something about it. The minute it is out of our hands then we are in trouble. Idon’t want to have to rely on anyone else.”