Ronald Koeman had said he would need four consecutive home wins to enter the international break with a smile. He goes into it under pressure instead, the boos of Goodison Park to accompany him and no closer to halting Everton’s regression after a summer spend of almost £140m. Burnley, for a fraction of the cost and with clearer thinking, move forward.

Jeff Hendrick’s fine first-half goal delivered the latest impressive away win for Sean Dyche’s team as the problems mounted for the Everton manager. Burnley have now won at Goodison and Stamford Bridge this season while drawing at Tottenham Hotspur’s temporary Wembley home and Anfield. Their problems on the road last season, when collecting a mere seven points from a possible 57, seem a lifetime ago. The same could be said of when Everton last played as an effective, settled and threatening unit.

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Wayne Rooney was dropped to the bench for the first time in the Premier League since returning to his boyhood club but it was only after his introduction that Everton attacked with quality or purpose. And that was not enough to break a supremely well-organised and disciplined Burnley side. Koeman claimed his position should not be under scrutiny because of the continued commitment of his players. It is under scrutiny, however, as he seems at a loss over what to do with them. It should also worry the Everton manager that he changed personnel and formation yet still oversaw a weak attacking display and a fifth defeat in eight games.

Not that Dyche has to worry himself with such pressures, having faced his own demanding start to the campaign and delivered Burnley’s best Premier League start. “The wins make a massive difference in the Premier League,” he reflected. “Away from home I don’t think anyone could have seen this start with the tough games we had. I think the players are shifting mentally. It is amazing what a difference it makes when you have that assuredness to go to these grounds. There are signs that we are improving.”

Everton had showed signs of improvement themselves until Hendrick struck a classy winning goal. The improvement ceased at that point. Koeman had argued his team’s poor form stemmed from a lack of confidence – an assessment Rooney publicly disagreed with following the draw against Apollon Limassol on Thursday – when a lack of pace, width and balance have been this season’s glaring faults. At Rooney’s expense, the Everton manager finally addressed some problems by starting Nikola Vlasic and Oumar Niasse alongside Dominic Calvert-Lewin in attack, although persisting with Gylfi Sigurdsson on the left did little for the team’s balance.

It is also a strange use of the £45m record signing’s talents but Sigurdsson had licence to drift inside and should have given Everton the lead as a result. The Iceland international twice had sight of Nick Pope’s goal, from balls across the penalty area by Vlasic and Niasse, but failed to connect cleanly on both occasions. They would prove to be Everton’s best chances and costly misses.

Burnley showed the composure that eluded Everton in the final third when they took the lead with an exquisite goal, one that Dyche may well refer to the next time someone applies the long ball label to his team. Robbie Brady instigated the breakthrough with a superb cross-field pass to Stephen Ward, who was overlapping on the left. Chris Wood headed Ward’s first-time cross to Hendrick, who found Scott Arfield before drifting into the box. Arfield released Ward and when the defender cut the ball back for the Republic of Ireland international he dummied Morgan Schneiderlin before placing a measured finish beyond Jordan Pickford.

Everton’s defence was static and badly organised, with Ashley Williams playing Ward onside and Schneiderlin weak in the challenge, but that did not detract from an outstanding team goal.

Koeman’s team offered little in response until Rooney arrived in the second half and the team shifted to a midfield diamond. Burnley absorbed the pressure comfortably with Ben Mee and James Tarkowski once again showing that Michael Keane’s £30m departure for Goodison has not had the disruptive effect many had feared. The visitors were almost presented with a second when Williams’s clearance cannoned off a claret shirt into the path of Arfield but the attacking midfielder went to ground too easily when he connected with the defender’s attempted recovery and was booked for diving. “I’m flummoxed by that,” said Dyche. “It looks like he gets a nick. Sigurdsson went down in the first half when there wasn’t contact and didn’t get booked. I’m not saying he dived, by the way. I just don’t think he needed to book him.”

Aimless shots from distance aside, Everton rarely threatened an equaliser and did not force Pope into a save until Calvert-Lewin shot straight at the keeper in the 87th minute. They claimed long and loud for two handballs by Matthew Lowton in the penalty area in the final stages. The second shout, from a Williams header, was rightly dismissed by the referee Jon Moss but the first, from Rooney’s flick, was a stronger claim, with the defender’s arm raised above his head. “You need to be lucky,” said Koeman. His luck is out, along with Everton’s form.