There are times in football when sacking a manager becomes an inevitability. Arsenal are not yet at that point but Mikel Arteta's position continues to be a matter worthy of scrutiny. The Spaniard came in for plenty of criticism in the aftermath of his tactical set-up for the Londoner's last away game – the 2-0 defeat at rivals Tottenham – here they were more pragmatic but still ended up losers.

Arsenal's subsequent games since that chastening experience have hardly provided evidence that a radical change in fortunes is to come. And, yet, it is hard to say with any great certainty that Arteta is at fault. Indeed if Arteta is to spend his time dodging brickbats for his decision-making there should still be recognition that it was his masterplan they followed in defeating Chelsea and Manchester City on their way to lifting last season's FA Cup.

Arsenal's problems are much more ingrained than their manager. For example, Arteta did not choose to splurge £72m on Nicolas Pepe from Lille last summer. Pepe is a case in point, when then director of football Raul Sanllehi thought he was being extra clever in hinting that he had limited funds to work with in the summer of 2019, he did so with one eye on the big catch that Pepe appeared to be. Arsenal fans hailed the coup, stealing in to snatch away one of Europe's most highly prized talents, giving a bloody nose to the continent's big guns and some of the Premier League's elite in the process. The reality has been somewhat different. Sanllehi paid for his profligacy with his job, leaving Arsenal earlier this year following an internal review into the signing.

Little wonder. The Ivorian winger has scored 13 goals since arriving in English football, four of which have come against fodder in the Europa League. Yet, he is not alone in failing as a big-ticket purchase at the club. Meanwhile, the £1.1m a week that goes on wages to Pierre Emerick Aubameyang, Willian, David Luiz and Mesut Ozil could have been put to better use, perhaps on building the kind of spine Arsenal have lacked since their title-winning team of 2004. If that side was the Invincibles this one – sitting in 15th place in the table this morning - might be better termed the invisibles.

Who is to blame? The board undoubtedly. Too many players are not good enough, the requisite spending needed to transform Arsenal into title challengers again has proved too rich for Stan Kroenke's blood ever since he bought a controlling stake in the club in 2007.

Expensive flops, cheap alternatives in key positions and the failings of a once-vaunted youth system are a toxic mix. Alex Iwobi probably can't be placed in that latter category since he yielded up to £34m in rising fees when he left Arsenal for Everton in the aftermath of Pepe's arrival but the fact that he was dispensable says it all.

Iwobi has established himself as something of a regular at Goodison Park but his output has actually regressed since his arrival on Merseyside with just three goals and four assists prior to the kick off here. That said, he stuck the ball on Dominic Calvert-Lewin's noggin for the opener, albeit via the aid of a significant deflection off Rob Holding as the ball spun past Bernd Leno in the Arsenal goal after 22 minutes.

The visitors struggled for a foothold in the game but, on a rare foray forward 11 minutes later, the ball broke for Ainsley Maitland-Niles in the area and when Everton's Tom Davies took an exaggerated swipe he clattered the Arsenal man's shin. Pepe sent Jordan Pickford the wrong way to add to his tally, restore parity and briefly change the atmosphere.

But, having lost two players in the previous two games to red cards, Arsenal were fortunate that Dani Ceballos remained on the pitch for a studs-down-the-calf stamp on Yerry Mina.

Mina demonstrated that he was uninjured in the challenge – perhaps a factor that kept Ceballos on the pitch – by leaping highest at the front post to flick Everton back into the lead following Gylfi Sigurdsson's corner seconds before the half-time whistle. Inexplicably, Pepe had been detailed to mark the lanky Colombian and was a poor second as Mina outjumped him with ease.

There was much more endeavour from Arsenal after the interval, notably on the left where Kieran Tierney and Bukayo Saka – if only Arteta had more in the manner of these two – worked in tandem to create a number of crossing opportunities in behind Mason Holgate. Indeed, most of their penetrative attacks came from this flank, but it was the failings of others that let them down.

The closest Arsenal came to equalising was when Luiz's shot into the turf was deflected on to the angle of bar and post.

Everton looked content to sit deep and spring counters and on a couple of occasions Ben Godfrey, playing as an auxiliary left-back, caused a degree of discomfort for the Arsenal backline by galloping forward – twice when Pepe ceded possession deep in opposition territory. It was little surprise when – having skewered a shot yards over the bar – he was replaced with 20 minutes to go. Penalty aside, it was another anodyne offering from the 25-year-old.

The Arsenal back four stood firm but even then Michael Keane drifted into the penalty area unchallenged at a set-piece and should really have nodded in the killer goal. In the closing 10 minutes, in forays spearheaded by Tierney and Saka, Arsenal looked more capable of scoring than they had done at any other spell in the game and Pickford had to make a smart stop from the latter after the former had slipped him in.

Yes, this was better but it is results that count. Almost exactly a year ago, Carlo Ancelotti and Arteta watched from the stands as their newly inherited sides played out a 0-0 draw at Goodison Park. Losing this time around – to confirm Arsenal's worst start in 46 years and leave them five points above the relegation zone with a game more played – can only be viewed as a giant backward step by the latter.