Carver became Newcastle boss on an interim basis when Alan Pardew left for Crystal Palace shortly after Christmas, but the team suffered an alarming run of form and lost eight games in a row.
In the final game of that run the Magpies lost 3-0 to Leicester and Williamson was shown a straight red card, which prompted Carver to question whether he had done it on purpose.
However, he told The Telegraph: "I embarrassed Mike Williamson and I embarrassed myself, but I still believe I did it for the right reasons and I embarrassed him into performing the next time he played. I apologised to Mike for going public. I had to go and find him to go through it.
"But Mike was fine and after the two-match suspension, he actually played well."
Newcastle survived, but Carver was dismissed shortly after the season ended.