Football Association board member Heather Rabbatts has expressed her "sadness and anger" at the reports club doctor Eva Carneiro has left Chelsea.
Carneiro is reported 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.
Press Association Sport claims it is likely that she will launch a claim for constructive dismissal.
Rabbatts said Carneiro had been subjected to verbal abuse, which the FA is probing, and criticism after she went on to the pitch to treat Eden Hazard -- Chelsea were then temporarily reduced to nine men late on against Swansea, with the scoreline at 2-2, 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 had her role with the club reduced 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.
Also on Tuesday, Chelsea striker Diego Costa was banned for three matches for violent conduct following an incident in Saturday's 2-0 win against Arsenal.