Sam Allardyce has been imploring his players to “respect the point” ever since taking up the reins at Crystal Palace back in December, and on this evidence they are taking note. There was anxiety to endure over the last few minutes here as Leicester City, infuriated at having cast away a two-goal lead so wastefully, flung everything at the hosts in their eagerness to force a winner. A few months back, Palace might have wilted. Yet there is strength now where, only recently, fragility was all around.

Danny Drinkwater fizzed Leicester’s best late chance just wide as Mamadou Sakho and Martin Kelly heaved to repel the barrage of centres and Jason Puncheon screamed instructions. Palace may have swarmed all over the visitors in the period immediately after falling two goals behind, missing as many presentable chances as they converted, but there was a deep sense of relief at the final whistle.

“It was a great point for us, a fantastic point,” offered Allardyce, with his side now seven points from the bottom three with a game in hand and a considerable advantage in terms of goal difference. “When you consider we scored two goals against Leicester, where Atlético only scored a freak penalty which wasn’t a penalty … it showed what we’re about.”

Leicester will need to be more resilient than this in Tuesday’s quarter-final return leg against the Spanish side. Their best player here was Robert Huth, who followed up his early headed goal with a staggering series of timely blocks and interceptions – there were eight from Christian Benteke, Wilfried Zaha, Puncheon and Luka Milivojevic – but the German is suspended for next week. The sight of Yohan Benalouane cramping up will have concerned Craig Shakespeare, with Christian Fuchs an unconvincing replacement at centre-half once the Tunisian had limped from the fray. Hope is still being pinned upon Wes Morgan featuring for the first time since the match against Sevilla in mid-March.

Jamie Vardy celebrates scoring for Leicester. Photograph: John Sibley/Action Image via Reuters

“It looked better yesterday,” said the City manager of his absent captain, who has been suffering from back trouble since the last-16 tie. “He trained with the group for the whole session on Friday, and I hope he joins in with the rest of the group again on Sunday. It’s a big ask for him because it’s a difficult injury to get over, in terms of power and spring for a centre-back. But we’ll give him every opportunity and, with the medical staff, we’ll see what their feelings are.”

At least Benalouane should be fit, for all that he was traumatised at times by Benteke’s power in the air. It was the Belgian who had leapt above the centre-back to meet the excellent Andros Townsend’s delivery and power home Palace’s equaliser, though City were outraged the goal was not disallowed with the forward “riding”, according to Shakespeare, on the defender’s back.

That completed the comeback sparked by Yohan Cabaye’s finish, the Frenchman perfectly placed to meet the loose ball after Jeffrey Schlupp’s shot had deflected off Danny Simpson. “Psychologically the players are in a far better place now than when I first arrived,” said Allardyce. “A player’s brain has to be functioning in the correct manner for his ability and skills to flourish. Our mental strength has increased in our decision-making process, and our fitness with it. Our quality, belief and determination have come shining through. Results are proving that now.”

Yet they had been forced to rally from a two-goal deficit here, Leicester having eased into an authoritative lead with a display that evoked last season’s triumphs. Huth’s early header from Fuchs’s throw-in had set the tone, the German rising above Joel Ward while Milivojevic dithered. “We’d practised defending against that here on the pitch yesterday,” said Allardyce, “but the players forgot. It’s that simple. They weren’t anywhere near where we put them, sadly, which is why he ran in with a free header and scored.”

The visitors’ second was just as trademark, with Townsend’s corner cleared out of City’s penalty area for Riyad Mahrez, holding off Zaha, to claim and liberate Jamie Vardy. The striker scuttled into the home half, tormenting Schlupp, a former team-mate, before cutting inside the full-back and curling his finish, via Wayne Hennessey’s fingertips, into the far corner. It was the forward’s sixth goal in seven games since Claudio Ranieri’s sacking, and really should have signalled the end of the contest as thoughts drifted back towards Europe. But there is more about Palace these days. Safety is edging ever closer.