Crystal Palace have no immediate plans to change their manager - but Pierre Sage is under increasing pressure following their 5-0 thrashing at Brighton on Sunday.
Palace find themselves 14th with seven points from seven games and Sage was unable to give assurances he had the club's full support after such a bitter defeat to their rivals.
Chairman Steve Parish recently stated the club was on "high alert" during the transitionary process from the era of Oliver Glasner into the new one under Sage, which includes a number of new players and a first Europa League campaign.
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Asked after the defeat whether he would be given time to turn things around, Sage said: "I don't know.
"I just want to apologise to the fans because it's not normal to show this face for this club against this other club, and we are not at the level we expected.
"I am really sorry for that because I know how important it is for them.
"We didn't show that today it was really important for us too. We didn't understand in which context this game was played."
Sage has come under fire for his attacking approach at Palace, who have the worst defence in the Premier League after conceding 17 goals in seven matches.
Palace's defensive unit took a hit over the summer with the sales of Daniel Munoz and Maxence Lacroix, both of whom were big figures in the club's success under Glasner.
Palace signed central-defenders Axel Disasi and 18-year-old Honest Ahanor on loan in the summer to replace Lacroix and Marc Guehi, who left to join Manchester City in January of this year.
Anan Khalaili was brought in from Union Saint-Gilloise initially to compete with minutes for Munoz but his arrival ended up paving the way for the Colombian to leave.
Crystal Palace's next five matches
Sunday 25th October 12:30pm Kick off 2:00pm
- October 22: Besiktas (A), Europa League
- October 25: Newcastle (H), Premier League - Live on Sky Sports
- October 28: Fulham (A), Carabao Cup - Live on Sky Sports
- October 31: Tottenham (A), Premier League
- November 5: Hoffenheim (H), Europa League