Sage struck a defiant tone during his post-match media conference as he addressed questions about his future for 20 minutes.
“I don’t have to convince the people around the club. I just have to convince the players to do their best to compete and to continue to improve,” he added when asked further about his job.
“After that, this kind of decision is for the chairman, to the owners, this kind of person.
“For me, the noise around the team, the noise around the club, it’s only noise.”
Palace have just seven points from their first eight league games in the post-Glasner era.
After losing to Everton and Manchester City in their first two matches, Palace won at Fulham before losing at home to newly promoted Ipswich.
They secured a rare clean sheet in a goalless draw at Leeds before coming from behind to beat Nottingham Forest at Selhurst Park on 11 October.
That was their last win.
They have since lost at his former club Lyon in the Europa League, and Brighton, before drawing 2-2 against Besiktas in Istanbul on Thursday.
However, patience is clearly wearing thin after fans reacted to the latest defeat by Newcastle.
In addition, Palace have the worst defensive record in the Premier League after conceding 19 goals in eight games.
Their next Premier League match is at improving Tottenham next Saturday, before hosting Liverpool on 8 November going into the international break.
Palace’s first game back is at fellow strugglers Coventry City on 21 November.
Will Sage still be in charge by then?
French football expert Julien Laurens said Sage needed to be more ruthless.
“He’s a lovely guy. He’s maybe a little bit too nice at times,” Laurens, speaking to BBC Radio 5 Live, added.
“Remember when Crystal Palace beat Fulham earlier in the season? That was Palace’s first win of the season and he felt sorry for Fulham.
“You don’t feel sorry in this league. This Premier League is ruthless. It’s the top, top level. This is the best league in the world.
“You can’t feel sorry for the opposition you have just beaten, especially when this is your first win and you needed it badly.
“But this is the kind of guy that he is.”