1. Everton lose again, yet show improvement

Sacking Ronald Koeman is not yet a cure for Everton's ills, but their performance at Chelsea, especially in the second half, may not have closed the door on caretaker David Unsworth becoming the Dutchman's full-time replacement.

Losing at Chelsea ended hopes that a Carabao Cup run could provide distraction from the pain of being in the Premier League relegation zone, but Everton played with far more spirit, and significantly better organisation than in Koeman's final days.

The problem, as it has been since Romelu Lukaku's departure this summer, was putting the ball into the net. Dominic Calvert-Lewin's goal did not come until the depths of injury time, by which time goals from Antonio Rudiger and Willian had put Chelsea in full control.

In the 26th minute, Charly Musonda, one of Chelsea's next generation among a quintet of youngsters Antonio Conte had selected in his starting lineup, drifted the ball to the right-hand post before Antonio Rudiger's header looped back across goal and into the far corner.

Once Chelsea went ahead, Everton laboured to the end of the first half like they have throughout their torrid season so far. Wayne Rooney was at centre-forward, the position where he struggled in his later Manchester United years, while Aaron Lennon and Kevin Mirallas, nominally playing off him, were often too far away to make anything of the balls he fought for.

A marked improvement at the beginning of the second half suggested Everton might find a way back, Mirallas' cushioned header found Rooney with only Willy Caballero to beat, but the shot was hit straight at Chelsea's backup goalkeeper.

Soon after that, Caballero was hustled into a mistake by Tom Davies that he had to recover from and then saw a series of Everton chances. Phil Jagielka flicked a header from a Leighton Baines free kick that Caballero had to claw away, then came a shot from Mirallas that had to be palmed from danger.

Chelsea were clinging on against an opponent playing with an intensity that had been so lacking during the final weeks of Koeman's regime, and especially in Sunday's 5-2 defeat to Arsenal; a tracksuited Unsworth barked orders from the sideline.

Rooney dropped deeper after the introduction of Calvert-Lewin as a centre-forward, but almost ended up supplying Michy Batshuayi with Chelsea's second goal with a no-look back-pass. It took a last-ditch tackle from Jagielka and the bottom of the post to spare Rooney's blushes for his last action before being replaced by Oumar Niasse.

The goal that Unsworth hoped for eventually came, but too late for this to be a night of redemption.

2. Unsworth states his case

Unsworth's ambition to land the Everton job on a permanent basis had been made clear during his prematch press duties. His team selection, a mix of senior professionals and graduates from the youth setup where he has been working since 2013, was a statement of intent that took a while to pay off, but ended up giving Chelsea a scare.

Width in a 4-3-3 was added by Lennon and Mirallas. It looked designed to be the opposite of Koeman's approach, where a surfeit of playmakers in a 3-4-1-2 had lately led to a disorganised mess. Pointedly, Unsworth had picked a team without a No. 10, leaving Gylfi Sigurdsson on the bench while Davy Klaassen was omitted altogether.

At Finch Farm, Everton's training ground, it is hoped Beni Baningime, a 19-year-old Congolese midfielder, can become the club's answer to Kante and eventually supplant Idrissa Gueye, suspended after his red card against Arsenal.

Baningime showed courage bordering on the foolhardy and crunched into challenges, with Ethan Ampadu the recipient of one particularly hefty tackle at the start of the second half, in a highly promising debut. Players like him and Davies, effervescent and hard-running as ever, probably hold the key to Unsworth achieving his ambition and being handed the chance to bed in the next generation of Evertonians.

3. Drinkwater makes his bow

Chelsea have been shorn of N'Golo Kante, who is not expected to return from a thigh problem until next month, but when he does return he should have Danny Drinkwater, his former Leicester partner, alongside him after the £35 million midfielder managed his first 60 minutes for his new club.

So far this season, Drinkwater's measure as a player has been marked only by Leicester's further decline this season without him. The former Manchester United trainee clearly looked up to Paul Scholes and Michael Carrick in his Old Trafford days and plays in a similar style: head up, thinking a pass ahead.

Among Conte's squad, Cesc Fabregas alone provides creativity from the centre of midfield, though Drinkwater has much more bite in the tackle, and contributed heavily to Chelsea's dominance of the centre in the first 45 minutes.

Though he had a promising first half, Drinkwater tired quickly and Chelsea's control faded in the centre. He was replaced by Fabregas just past the hour mark, suggesting it could be a while yet before Conte gets full use of Leicester's former engine room.