The FIA confirmed prior to the United States Grand Prix in November that Hartstein, who took over the role from the late Sid Watkins in 2005, would not have his contract renewed and did not go into detail as to why.
Hartstein has since taken to Twitter to demand answers from the FIA.
"It's taken a while, but I am righteously pissed off. I might launch a crusade to get some answers, or get my f**king job back, or let the world know what's REALLY going on on the medical side of the FIA", he posted on the social networking site on Monday.
"Understand this: I am NOT bitter or sad. I am seriously angry. And that's bad."
F1 drivers were perplexed as to why Hartstein's services were dispensed with. Pedro de La Rosa commented in Brazil that "All I can say is that Gary is someone who we feel extremely comfortable with. We are surprised and definitely looking into who will be his replacement."
The FIA has yet to announce Hartstein's successor.