Crystal Palace conceded three goals in the opening 10 minutes on their way to a heavy 5-0 defeat against Brighton, marking their worst loss to their rivals since January 1956.
Sage, who took charge in the summer after a successful stint at Lens, shouldered full responsibility for the dismal performance and poor tactical preparation.
The heavy loss leaves Palace 14th in the Premier League table, having conceded 17 goals, which is the most in the top flight so far this season.
When asked if he would be given time to turn things around, the French manager replied that he did not know, while offering a sincere apology to the club's fans.
