The Blues were in decent spirits heading into their clash with Antonio Conte’s defending champions, then.
Ultimately, however, Everton’s positive mindset and approach couldn’t overcome either their own tired legs or Conte’s irresistible team.
Paul McNamara looks at five talking points from a difficult afternoon in west London…
Blues made of the right stuff
Everton’s manager and players could have legitimately trotted out any number of reasons for losing at Chelsea.
Chief among them, of course, the fact this was a third away game in a week which had involved 3,500 miles of travel by air and road for the Blues.
There has been no ‘gimme’ in that trio of matches, either. And the hardest of the lot was reserved for last, a clash with the English champions on a broiling afternoon in the capital.
But the collective message from Everton’s camp post-match was unequivocal.
“Not good enough,” concluded Koeman, as he dissected the Blues’ first-half performance. Ashley Williams, meanwhile, was not prepared to flag up his team’s crowded schedule as reason for the defeat – and Mason Holgate echoed manager Koeman’s verdict when he bemoaned Everton’s “slow start” against Conte’s side.
Nevertheless, the Toffees’ never threw in the towel. Quite the opposite in fact; they stuck at it and, within touching distance of their superb opponents late in the game, came off the ropes and started swinging.
Sandro Ramirez, Idrissa Gana Gueye and Williams all spurned opportunities of varying degrees of difficulty.
Williams was furious with himself for missing the target after Gylfi Sigurdsson’s wonderful, dipping cross had landed on the unmarked defender’s head in front of goal.
Had Williams directed the ball inside Thibaut Courtois’s left-hand post, rather than a yard wide of it, we would have had a grandstand finish on our hands.
No question, Chelsea were worthy winners. But Everton’s refusal to roll over kept the contest alive.
In the circumstances, that deserves a tick in the credit box, at least. Not that Koeman or his players were remotely interested in such consolatory approbation.
Steep learning curve
Koeman talked after Thursday’s match in Croatia of his wish that Everton’s troop of young bucks would use the experience of playing European football to accelerate their development.
Dominic Calvert-Lewin was among those namechecked by the manager, as he animatedly discussed the value to his emerging stars of sampling nights like those in Hajduk Split’s vibrant Stadion Poljud.
What Koeman saw from the forward three days later would have pleased him, then.
Calvert-Lewin was sent on with 28 minutes to play at Stamford Bridge and greeted by circumstances entirely different – but no less difficult – from those he encountered when he played from the start during the week.
The 20-year-old had reverted to a wide role as Everton looked to finish off Hajduk. His remit on Sunday was to alter the course of a match against the best team in England.
And the evidence of the game’s closing stages stands as testament to Calvert-Lewin’s influence from the bench.
Operating as a striker, he immediately set about discomfiting the hitherto unflustered Antonio Rudiger, while German Rudiger’s fellow defenders David Luiz and Cesar Azpilicueta were knocked back on their heels by the speedy Calvert-Lewin’s direct running.
Suddenly Everton had more space in Chelsea’s defensive third. In turn, the Toffees’ fashioned a steady stream of chances, without being able to score the goal that would have really jolted the hosts from their comfort zone.
Koeman keeps setting the bar high for Calvert-Lewin, a ploy the manager would not entertain if he was not confident his young charge could cope with his demands.
The last word on this one goes to Koeman, who said: “I am really impressed by Dominic and that started last season, not today.”
Welcome back Sandro
Sandro faced a unique challenge among Everton’s team at Chelsea. While most were managing weary bones, the Spaniard had to find his match feet after two weeks on the sidelines.
The 24-year-old’s Goodison Park career suffered a false start when a heel injury suffered during a promising debut against Stoke ruled him out of both matches against Hajduk Split and the meeting with Manchester City.
There is no good time to be absent but for Sandro, settling into a new country and adapting to an alien football environment, this was the most untimely and unwelcome setback.
For Everton, too, given their need for fit bodies with games coming thick and fast.
What a boost, then, for Koeman, Evertonians and, above all, the player himself, that Sandro was ready to feature on Sunday.
He poured an enormous amount of effort into ensuring he was able to return before the international break, then did likewise in an unforgiving, lone striking role at Chelsea.
Sandro will rue the fact that his major scoring chance came along when fatigue was setting in – and shortly before he was withdrawn on 62 minutes.
Nevertheless, that opportunity arrived because of the player’s intelligent run to make himself available for Wayne Rooney’s through ball.
On a day when the nature of the game dictated that much of his work went unseen, it was a reminder of what the former Barcelona attacker could potentially bring to the party.
It doesn’t get much easier for Everton next time out – Tottenham visit Goodison Park on 9 September.
Koeman would relish having a ready and raring Sandro back in the fold for that one.
They don’t come tougher
There is a case to be made for Chelsea away being the hardest date on the Premier League fixture card – fewer than 72 hours after playing in Split or not.
Conte’s side won the title three months ago. It stands to reason, therefore, that they are the country’s most formidable outfit.
In a peculiar sort of way, Chelsea achieved the feat of slipping under the radar, somewhat, as they bestrode England’s top-flight last season.
But Everton twice last season witnessed first-hand why Chelsea were bound for a second title in three years.
Koeman is a confirmed admirer of Conte's side and shares plenty of his footballing ideals with the London club’s Italian boss.
Certainly, the two men are cut from the same cloth with respect to the application to the cause they demand from their players.
But while Koeman’s men pitched up at Stamford Bridge with little in the tank, the refreshed home team were full of gas.
Attacking duo Willian and Pedro were absolutely electric, both men a bundle of energy, industry and skill. Victor Moses and Marcos Alonso played the wing-back roles exactly as they were designed.
With his mix of shrewd recruitment and trust in youth, Koeman is building an Everton side which – in time – could prove similarly potent.
The Blues boss conclusively separated Everton from the 13 teams beneath them last term. Here was a reminder of the distance of travel to the very top.
On which note – the season so far
Everton’s defences were not breached until the 82nd minute of their fifth competitive match this term.
Their first defeat came in outing number seven – and at the home of the aforementioned, exceptional Chelsea.
This all points to things heading firmly in the right direction.
Koeman has astutely navigated a first month of the season unprecedented for its demands on an Everton team.
The Blues’ European campaign remains alive and kicking, for starters.
And the significance of the opening-day Premier League victory over Stoke cannot be overstated. With an audible buzz around the Club and a demanding run of fixtures on the horizon it was imperative for Everton to beat Mark Hughes’s team.
That they did so courtesy of a goal from the returning Wayne Rooney only added to the value of the victory.
A whole host of Rooney’s fellow new boys have settled into Goodison Park as if to the manner born. Jordan Pickford and Michael Keane, for example, have made light of their respective price tags and both feel part of the Everton furniture already.
Those two players were excellent in the Blues’ draw at Manchester City, a match which signalled further how Koeman is steadily transforming his side into one equipped to compete with the best.
A perfectionist, the Everton boss won’t be wholly satisfied with the opening phase of this season – you don’t have the career Koeman has had if you shrug off any defeat as immaterial.
But he could certainly have justification for reflecting with more than a smidgeon of contentment on how things have played out to this point.