Carneiro is understood to have parted company with Chelsea following the incident on the opening day of the season when she was criticised by manager Jose Mourinho.
It is thought likely she will launch a claim for constructive dismissal.
Rabbatts said Carneiro had been subjected to verbal abuse and criticism after running 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.
“News of Dr Eva Carneiro’s departure from Chelsea FC makes me feel sadness and anger,” said Rabbatts, who is chair of the FA’s inclusion advisory board.
“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 on August 8.
Rabbatts said she had been effectively demoted for doing her job properly.
A Chelsea spokesman said he could not comment on internal staffing matters.
Rabbatts added: “On the 8th August Eva fulfilled her duty as the senior medic and responded to the referee to enter the field of play to treat a player.
“Any other response would have been a dereliction of her duty and a breach of GMC guidelines as confirmed recently by the organisation of Premier League doctors.
“In acting properly she was then subject to verbal abuse and public criticism and in effect demoted by her removal from the bench.
“Her departure raises a serious question on how players are safeguarded if their medical support is compromised.” Carneiro was also the victim of sexist abuse from opposing fans last season.
The FA is still investigating a complaint from a member of the public that Mourinho used sexist language towards her after the incident on August 8 — he denies doing so.
Rabbatts added: “In addition, as chair of the Inclusion Advisory Board, I have a responsibility to support women in the game and Eva has been a role model for many girls and women who aspire to work in football. Her treatment sends all the wrong messages.
“The footage of the abuse she has endured in silence from the stands during her career is something we should all be ashamed of.
“Being passionate about the game is also about standing up against abusive chanting, bullying and insults to a fellow professional.
“As a member of the board of the FA, I can make no comment on the FA investigation currently under way and this is rightly a matter for the regulation team.
“However, I believe that all those who have an interest in these issues and who have a duty to safeguard relevant policies and procedures raise their voice in support of Eva.
“I hope that Eva’s own situation can be resolved quickly and positively, that she will be able to continue to work in a senior position within the game and that steps are taken to ensure that professional integrity is protected and women are properly encouraged to be a part of our national game, including at elite level.”
The issue of team doctors has been discussed by the Fifa medical committee as a result of the incident.
Earlier this month, FA chief executive Martin Glenn said: “We work to a Fifa mandate on medical support. The duty of the doctor is to the player, not the employer. It is the Hippocratic oath.”
Meanwhile, Chelsea striker Diego Costa has been banned for three matches after a charge of violent conduct during Saturday’s 2-0 win over Arsenal at Stamford Bridge was upheld.
Costa had denied a FA charge over the incident, not seen by referee Mike Dean, in which he appeared to raise his hands to Gunners defender Laurent Koscielny.
An FA statement read: “An FA charge against Diego Costa for violent conduct not seen by the match officials but caught on video has been found proven following an Independent Regulatory Commission hearing.
“The Chelsea forward will, therefore, serve the standard penalty of a three-match suspension with immediate effect. The charge, which the player denied, was in relation to an incident involving Arsenal’s Laurent Koscielny in the 43rd minute of the game on Saturday [19 September 2015].”