Pierre Sage has been granted more time to fix Crystal Palace’s defensive issues but warned things must improve quickly after Sunday’s humiliating 5-0 defeat at Brighton.

The Frenchman’s future was in serious doubt after his side conceded three times inside the opening 10 minutes before equalling the 70-year-old record for the club’s heaviest loss against their arch-rivals. The thrashing means Palace have conceded the most goals in the Premier League: 17 from seven matches.

The chair, Steve Parish, is understood not to have been fully convinced by Sage since the 47-year-old was appointed to replace Oliver Glasner in the summer. Parish is believed to have considered parting company with Sage on Sunday after 10 matches but decided against a change given that Palace are 14th and not in immediate danger.

Sage is expected to remain in charge not only for Thursday’s Europa League game at Besiktas but Sunday’s Premier League match against Newcastle. However, it has been made clear to the former Lens manager that his position is under heavy scrutiny. Kieran McKenna, who Parish approached while the Northern Irishman was at Ipswich, and Thomas Frank will be among the contenders if Sage is sacked.

Tensions between Sage and Parish date to the summer transfer window when Palace failed to land the manager’s main targets to replace Maxence Lacroix in central defence. Two loanees, Axel Disasi and the teenager Honest Ahanor, were signed instead from Chelsea and Atalanta respectively. Palace also missed out on Malick Fofana to Sunderland on deadline day despite Sage making the Belgium forward, who he coached in Lyon’s youth teams, a priority. Palace instead signed Darío Osorio on an initial loan and the Chile forward has played only a handful of minutes.

Parish was unhappy with Sage’s treatment of Jaydee Canvot after the France Under-21 international was dropped from the squad for the home defeat by Ipswich last month. He is also understood to have been angered by Adam Wharton being substituted in that match after Disasi was shown a red card in the first half.

Some behind the scenes at Palace have been pushing for Sage to be sacked, but Parish is thought to recognise the headache caused by Disasi’s three-match suspension and injuries to Chadi Riad and Takehiro Tomiyasu and would prefer to give him an opportunity to turn things around.

Chris Richards has apologised to Palace supporters after failing to acknowledge them after the Brighton game. “I want to apologise for walking off after the game,” the USA defender wrote on Instagram. “I was emotional and embarrassed with the result – I know how much this club means to all of you. We have to take responsibility, do better and show that on the pitch.”