Antonio Conte shared a joke with Lisa, the dedicated host of the media room, as he politely asked for some sweets. That moment of brevity apart, the Chelsea manager was a model of frustration as he digested two points dropped and a performance that highlighted the champions’ over-reliance on the magic of Eden Hazard.

Another sign of progress for Everton under Sam Allardyce was another afternoon of torment for the Chelsea manager. His team dominated at Goodison but were stifled by a well-drilled Everton defensive display with their two £30m summer signings, Jordan Pickford and Michael Keane, excelling.

When the visitors did find a way through, a finishing touch and fortune deserted them. Hazard was a mesmerising presence but Álvaro Morata’s one-match suspension proved costly against a rearguard whose resilience and confidence has been restored under their new, unbeaten manager.

“When you dominate possession, shoot 26 times, but only eight on target, hit the crossbar and a defender clears twice off the line, for sure you must be disappointed,” said Conte. “We deserved to win.

“I consider Everton to be the best team in this league after the top six and we played with great personality and intensity, and with great concentration because they defended very deep. But if you want to win this game you must score and you must be more clinical.”

His assessment brooked no argument and he departed with a request for a few more sweets.

There were echoes of the recent Merseyside derby draw as Allardyce’s team were encamped deep in their own half against a fluent attacking unit and reliant on Dominic Calvert-Lewin turning water into wine up front. As at Anfield, they managed to frustrate the team dominant in possession. Conte’s body language also betrayed an annoyance with the movement and final ball his team. Hazard excepted.

The Belgium international took the game to Everton, shouldering responsibility to lead the Chelsea line, but the supporting cast of Pedro and Willian struggled to exert the same influence and were withdrawn. Credit was due to a changed Everton defence and improved performances from Morgan Schneiderlin and Keane, the latter producing his best game for the club.

Illness swept through the home squad before the game and sidelined Wayne Rooney. Ashley Williams and Mason Holgate dropped to the bench as Allardyce rotated with the festive schedule in mind. The two defenders have epitomised Everton’s recent recovery but their absence was not felt thanks to the contributions of Keane and Phil Jagielka, who made two goalline clearances in quick succession to deny Tiémoué Bakayoko and Willian from Chelsea’s first clear opening.

The visitors’ best chance of the first half fell to Pedro when released by Bakayoko but Pickford tipped his rising drive over the crossbar.

Everton’s hopes of alleviating the pressure centred on long balls up to Calvert-Lewin and a requirement on the young centre-forward to hold up play against three Chelsea defenders. It was a tall order. Change was necessary and Allardyce made a double substitution at the interval to match Chelsea’s 3-4-3 formation. Williams and Sandro Ramírez replaced Tom Davies and Aaron Lennon respectively. However, five minutes into the new system, Everton lost Idrissa Gueye to a hamstring injury that could sideline him for a fortnight. Gueye had impressed in the battle of the midfield shields with N’Golo Kanté and his departure was a blow to Everton’s resistance. Yet resist they did.

Pickford enjoyed another impressive afternoon. The keeper saved well from Pedro, Hazard and Antonio Rüdiger as the visitors pressed for a breakthrough. When he was finally beaten it was by his own player, Williams, who met Victor Moses’s cross with a header that Morata would have been proud of. Fortunately for the Wales captain, his effort cannoned against the bar and clear.

Everton almost stole victory in the 90th minute when Keane rose highest to meet Gylfi Sigurdsson’s corner but his header was a yard over.

“We scrapped it out, there is no doubt about that,” Allardyce said. “The changes I made to try and get up the pitch more didn’t work as I would have liked but defensively I can’t knock the team in terms of the effort and commitment and organisation. Our defending is outstanding compared to when I arrived.”