Already a man down after goalkeeper Thibaut Courtois had been dismissed in the first half, Chelsea faced a short period with just nine players as, according to the rules, Hazard left the pitch to receive treatment.
The 42-year-old Carneiro soon had her responsibilities curtailed before deciding to leave the club.
Le Saux condemned Mourinho's behaviour and said the Portuguese's handling of the situation had hurt the FA's attempts to push for equality in football and could even deter clubs from employing women in key roles.
"What concerns me most, given the work I'm doing for the FA, is the impact Mourinho's behaviour may have throughout the whole game. We're trying to deal with some very sensitive issues and to change the culture of the game," Le Saux told Thursday's edition of the Times.
"Some good people at the FA have taken a kicking after concluding there was insufficient evidence to charge Mourinho, whilst the whole furore may also deter women from becoming involved in football, as well as discouraging clubs from employing them.
"A lot of people are working very hard to get the game in a better place, but after the last few weeks it feels as if we've gone back 30 years.
"Mourinho doesn't seem to have reflected on the damage he's done to his own image, the reputation of the club and, more importantly, the reputation of the entire game," he added.
Mourinho, whose team lie 16th in the Premier League table, was given a suspended one-match ban and fined 50,000 pounds ($77,390) by the FA on Wednesday for criticising officials after his side's home defeat to Southampton on Oct. 3.
Meanwhile, Chelsea goalkeeper Asmir Begovic has joined a host of senior players in backing his manager during what the Portuguese has called the "worst period" of his career.
"He's not happy, of course. He doesn't want to lose," Bosnian international Begovic said.
"That's the only comforting thing: we have the best manager in the world. We believe in him and he believes in us. We will turn things around."
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
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