Football Association chairman Greg Dyke says Chelsea manager Jose Mourinho not apologising to Eva Carneiro was “clearly a failure of his personal judgement”.
Doctor Carneiro was dropped from first-team duties after an incident on the opening day of the season when she was criticised by Mourinho for going on to the pitch to treat Eden Hazard.
Mourinho was cleared by the FA on Wednesday of making discriminatory comments towards Carneiro. According to Sky sources, the FA approached Carneiro's legal representatives to ask if she wished to provide any evidence but thus far none has been forthcoming.
However, a letter from Dyke to FA council members following Wednesday's FA board meeting made clear his misgivings over Mourinho's behaviour.
Dyke says in the letter: "There have been some well-documented issues of late around equality and inclusion in the game, an issue where it is vital we continue to show clear leadership.
"I felt the handling of the case of the Chelsea doctor, Eva Carneiro, was a good example of this. We supported Heather Rabbatts' strong statement on the matter earlier in the month.
"Personally I don't think Mr Mourinho comes well out of the whole saga - he clearly made a mistake in the heat of a game, and should have said so and apologised. Instead he has said very little and Miss Carneiro has lost her job.
"Our regulatory team have investigated this and whilst Mr Mourinho has breached no rules it was clearly a failure of his personal judgement and public behaviour. This should be seen as such by the game."
Heather Rabbatts, an independent board member and the head of the FA's inclusion advisory board, said she had "major concerns" regarding the FA's disciplinary process in the case.
Rabbatts told SSNHQ: "The only person who has suffered significantly is Eva Carneiro. She's someone at the top of her profession and she's been doing her job brilliantly well and now she's lost her career she dearly loved. She's paid the price for doing nothing wrong.
"Eva Carneiro was punished for doing her job, which is an offence to human justice. The FA's reaction to the treatment of Dr Eva Carneiro has been seriously disappointing."