Carver could not disguise his anger at his players after Saturday's defeat, which leaves them just two points ahead of bitter rivals Sunderland in 18th, who have a game in hand. The loss was Newcastle's eighth in a row.
"I thought he meant it," Carver said in his post-match press conference.
"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."
A statement issued on behalf of Williamson was released by Refuel Performance Management on Sunday following the Magpies' 3-0 defeat at the King Power Stadium which left them in serious danger of relegation. Dutch full-back Daryl Janmaat was also dismissed to leave interim boss Carver fuming.
Williamson said in the statement: "I would like to take this opportunity to apologise to the Newcastle United supporters and my fellow team-mates for getting sent off during yesterday's game.
"There was absolutely no intent to hurt (Leicester's) Jamie (Vardy) or get sent off, but I recognise I should have been more composed and measured in my determination to win the ball. Unfortunately, it did the one thing that I never wanted to do, and that was hurt the team.
"Moving forward, I will do whatever I can to help my team-mates prepare for the next two games and fight to get back into the team when I'm next available.
"I've had the honour to play for Newcastle United for five years now, and I can genuinely say that I feel privileged to play for this football club. I would never do anything intentionally to hurt the team or its supporters."