The departure of club doctor Eva Carneiro and a three-match ban for striker Diego Costa overshadowed Chelsea's build-up to Wednesday's Capital One Cup tie at Walsall.
Football Association board member Heather Rabbatts expressed her "sadness and anger" at the news Carneiro had left Chelsea.
Carneiro is understood to have parted company with the Blues in the wake of the incident on the opening day of the season when she was criticised by manager Jose Mourinho. It is understood likely that she will launch a claim for constructive dismissal.
Rabbatts said Carneiro had been subjected to verbal abuse and criticism after she went on to the pitch to treat Eden Hazard - Chelsea were then temporarily reduced to nine men against Swansea as Hazard had to leave the field.
Head physiotherapist Jon Fearn did likewise and Mourinho said at the time: "I was unhappy with my medical staff. They were impulsive and naive.
"Whether you are a kit man, doctor or secretary on the bench you have to understand the game."
Rabbatts, who is chair of the FA's inclusion advisory board, said on Tuesday: "News of Dr Eva Carneiro's departure from Chelsea FC makes me feel sadness and anger.
"Eva was one of the few very senior women in the game, a highly respected doctor who has acted with professional integrity in difficult circumstances and whose skills have been highly praised by her colleagues, the club and governing bodies."
Carneiro has not been at Chelsea's Cobham training ground since she was removed from first-team duties shortly after the Swansea game. Rabbatts said she had been effectively demoted for doing her job properly.
A Chelsea spokesman on Tuesday said he could not comment on internal staffing matters.
The London club did have their say, though, on the three-match suspension dished out to Costa for violent conduct during Saturday's 2-0 Barclays Premier League win over Arsenal.
An FA regulatory commission made the ruling on Tuesday just hours after Gunners defender Gabriel won his appeal against a red card for confronting Costa after the incident in question.
Costa had denied an FA charge over the incident, not seen by referee Mike Dean, in which he appeared to raise his hands to Gunners defender Laurent Koscielny.
Costa's antics were widely criticised within the game, but Mourinho was eager to stress his player's innocence and will no doubt have more thoughts to add to the terse statement issued by the club on Tuesday night.
It read: "We are extremely disappointed with the FA regulatory commission's decision to suspend Diego Costa. We will await their written reasons before commenting further."
Both clubs still face an outstanding charge of failing to control their players, while Gabriel faces an additional charge of improper conduct for his reaction after being shown the red card.