PSG lost for the first time at home in the top flight this season, which was also their first loss at the Parc Des Princes since April 2021.
Karl Toko Ekambi and Arnaud Kalimuendo scored for the visitors either side of half time as PSG's lead at the top of the table was whittled down to seven points.
Pressure has been building on Galtier ever since Bayern Munich knocked PSG out of the Champions League and this defeat has done little to calm tensions.
PSG were missing a host of first team regulars for the encounter, including Neymar, Marquinhos, Achraf Hakimi, Presnel Kimpembe and Sergio Ramos, and Galtier believes that could be a factor for the loss.
"I came for this project for two years, but we speculate on my future," Galtier told reporters post-match.
"My only obsession is to be champion. This match will perhaps cause my management to reflect, but we have to put things in context.
"This match should not call everything into question. There are no excuses but there are reasons. There are 10 matches left, we are ahead in Ligue 1.
"Losses always upset us. Afterwards, everyone has their reading of the game. You have yours and I have mine.
"In the current context, with so many absences – though it is not an excuse – we knew that we would have defensive fluctuations."
"The players gave everything compared to what they had in their legs.
"You get the feeling that the players didn't give their all, but that's not how I feel.
"When a player walks into the locker room and knows that eight players are missing, and he sees young guys he has only seen once or twice before...
"My players were invested, after going 2-0 down to a team like Rennes, there may be a little resignation. There is a lot of fatigue. These are not excuses, just contextual elements."