The manager was infuriated that Rayner had failed to flag for what he regarded as a clear penalty and condemned her presence on the line as "tokenism for politically-correct idiots".
"She should not be here," he said. "I know that sounds sexist, but I am sexist, so I am not going to be anything other than that."
"It is bad enough with the incapable referees and linesmen we have, but if you start bringing in women, you have big problems," he added.
"This is Championship football. This is not park football, so what are women doing here? It is tokenism, for the politically-correct idiots."
"Will I be the manager at the weekend? That is a question for the board."
Mike Newell, Luton Manager
Forty-eight hours after his outburst, Newell admitted his remarks had been ill-judged.
"I want to apologise publicly to Amy Rayner and to anyone else I have offended," he told reporters.
"The comments I made were ill-timed and out of order. I wanted to apologise privately before I apologised publicly, but I could not get hold of Amy Rayner."
Newell's apology came amid speculation that his job could be on the line at an emergency board meeting on Monday afternoon.
His public criticism of chairman Bill Tomlins has also got him into trouble.
Asked about his future, Newell said, "Will I be the manager at the weekend? That is a question for the board, but I am not going to resign."
Luton are currently ninth from bottom of the 24-club Championship.