The “perfect afternoon”, according to Ronald Koeman, although that depends on the shade of blue. For Tom Davies, Ademola Lookman and those of a royal hue, it was undoubtedly true as Everton produced the finest display and result of the Koeman era. For Pep Guardiola, by contrast, this was a harrowing, humbling experience. Manchester City were dismantled and their revered manager left searching for answers to the heaviest league defeat of his glittering career.

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Guardiola conceded the Premier League title is beyond his expensively assembled side after enduring the club’s biggest defeat against Everton for 31 years. “You’re getting sacked in the morning,” reverberated around a jubilant Goodison Park as the home crowd revelled in an uncomfortable return for John Stones and the emerging talents of Mason Holgate, the new signing Lookman and the outstanding Davies in particular. The Evertonians were pushing it, of course, but the City manager has bigger problems than the rarity of ending a league campaign without the championship on the evidence of another feeble defensive performance.

Romelu Lukaku opened the scoring with Everton’s first shot on target, a familiar story for City and one Guardiola admitted affected his players mentally, having started brightly. Kevin Mirallas struck a decisive blow moments after the restart and from that moment onwards the fortunes of Koeman and Guardiola, friends from their Barcelona days, veered in wildly different directions.

Everton’s day rose to a crescendo as the 18-year-old Davies opened his account for the club with an exquisite finish that his uncle, the former title-winning striker Alan Whittle, would have been proud to call his own. Lookman, signed in an £11m deal from League One Charlton Athletic, then became the second teenager to score his first Everton goal – within four minutes of his Premier League debut.

“Maybe that was the best in terms of it being a total team performance,” the Everton manager, Koeman, said. “How we played in the second half was really outstanding, really perfect. It might have been impossible to play at a higher level in every aspect of football.”

The worry for City was not only their limited reaction to falling two goals behind early in the second half but their manager’s admission that he “has to look for the best solution” to issues that have plagued his team for several months. Ten points adrift of the leaders Chelsea and languishing outside the Champions League places, City are toiling defensively while their manager insists a more clinical approach will alleviate inconsistencies and torment at the back. This was a defeat that also raised questions of theircharacter.

Guardiola described City’s first-half display as “exceptional” and they did impress until Lukaku scored his 13th of the season in the 34th minute. Raheem Sterling screamed in vain for a penalty after colliding with Joel Robles’s trailing leg as he attempted to round the Everton goalkeeper and the covering Leighton Baines. The referee, Mark Clattenburg, was unmoved. That came from City’s first foray down their left and the first of several quality deliveries from Kevin De Bruyne, who created another clear opening for the former Liverpool winger and David Silva. Both were wasted, so, too, a two‑on-one counterattack involving Sterling and Pablo Zabaleta – deployed as a roving central midfielder in the absence of Fernandinho, Fernando and Ilkay Gündoğan. Their generosity was punished ruthlessly.

The breakthrough arrived when Gaël Clichy gifted possession to Davies. The teenager pierced City’s defence with a superb pass into Mirallas, who cut the ball back invitingly for Lukaku. His compatriot side-footed a precise, powerful shot inside Claudio Bravo’s left-hand post.

Remarkably, it was the fourth time in the past seven league games that City had conceded the first shot on their goal. Guardiola had switched Stones, given a harsh reception, to the left of City’s central defence to combat Lukaku’s tendency to cut inside onto his favoured left foot. There was no City defender near the Belgium international when he converted and the tone for a feeble display at the back had been set.

Lukaku, who had carried Bradley Lowery – the five-year-old Sunderland fan diagnosed with neuroblastoma – on to the pitch before kick-off was involved in Everton’s second. His attempted through-ball was intercepted by Stones but the impressive Ross Barkley slipped the rebound into the path of Mirallas, who found Bravo’s far corner with an excellent finish – in keeping with the Belgian’s overall contribution.

Guardiola introduced Kelechi Iheanacho for Zabaleta in an attempt to cajole a fightback but City’s response barely flickered into life. Everton’s day simply got better and better.

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Davies, who had cleared a Clichy header off his own goal-line in the first half, put the contest beyond the visitors with a goal that encapsulated the many qualities he has shown since joining the senior ranks. First, he outmanoeuvred Yaya Touré and Clichy with a determined run down the right before playing the ball inside to Lukaku. Barkley took over, spotted that Davies had continued his run and released the teenager on the right of the penalty area. Davies clipped a delightful finish over the advancing Bravo and beyond Lukaku’s attempt to apply the final touch on the line.

Koeman brought on the £20m signing Morgan Schneiderlin and, so comfortable were Everton, January’s other recruit, the 19-year-old Lookman. The forward had been on the pitch less than four minutes when Séamus Coleman’s raid broke to him inside the area and, ignoring the right-back’s call for a return pass, he fired a low finish through the legs of the City goalkeeper. Guardiola’s men were routed, well and truly.