Chelsea team doctor Eva Carneiro's statement on social media was a "slap in the face" for Jose Mourinho, according to one of her predecessors.
But Ralph Rogers, Chelsea's first team doctor under Carlo Ancelotti, said the Facebook comment was not "ethical".
He added it will be "difficult" for the 41-year-old to regain Mourinho's trust.
Carneiro tended to Hazard after he was tripped in the final minutes of Saturday's 2-2 draw with the Welsh club, meaning the Belgium forward had to leave the pitch.
It reduced Chelsea to nine men as goalkeeper Thibaut Courtois had already been sent off and Mourinho afterwards said his medical staff were "impulsive and naive" and did not "understand the game".
Carneiro responded on Facebook by writing: "I would like to thank the general public for their overwhelming support. Really very much appreciated."
Speaking on BBC Radio 5 live, Rogers said: "You are support staff. You're not one of the stars. There's almost a slap in the face to the manager.
"Why would she go to social media? It's something we, as a profession, ethically should not be doing."
Carneiro now looks set to lose her place on the Chelsea bench for Sunday's Premier League match against Manchester City.
And Rogers, who did not question Carneiro's judgement and treatment of Hazard, added: "There has to be a very good relationship between the medical staff, or the physician, and the manager.
"The manager has to be able to trust the medical judgement he's receiving and when that trust is broken, where do you go? It's going to be difficult."
Eamonn Salmon, chief executive of the Football Medical Association - which represents professional medical staff in the sport - has backed Carneiro and physio Jon Fearn while Liverpool's former head of medicine Peter Brukner says Mourinho should apologise to the doctor.