The evidence to the contrary had been overwhelming for the previous 90 Goodison minutes but Unai Emery still felt inspired to make an impassioned claim that his Arsenal side will finish in the top four, and end the first season of the Arsene Wenger era by clinching Champions League football.
There had been little to support that claim as Phil Jagielka, drafted into the Everton starting line-up just minutes before kick-off, scored the only goal of a game that left Emery facing the prospect of collecting an unwanted statistical mark in his first season in the Premier League.
In the top four divisions of English football, no other side has failed to keep a clean sheet on their travels this season but, thanks to Jagielka’s 10th minute goal and a generally sub-par Arsenal performance, Emery’s side can make that claim.
Not that the Spaniard was anything but defiant in the wake of a result that leaves Arsenal with a worse away record than any team in the division’s top nine places.
“I think generally we are well,” claimed Emery.
“I don’t think, today we lost and we are very bad. It was a bad result, not a good performance today, but we are fourth.
“Before, I knew it was going to be difficult. After this result, I am thinking the same.
“After this result, we can be negative because it is three points lost, but it is in our hands, if we continue taking chances and opportunities, to be in the top four.
“We lost a big opportunity and today we didn’t show our our capacity to impose our game plan against them. So we’re going to think about our next game on Thursday, and our next league game against Watford, and if we can continue being consistent, we can win.”
It would have helped Emery’s cause, and lifted them into third place, had his team managed to collect at least a point at Goodison.
But his defence failed to heed the warning from an early Lucas Digne’s long throw-in and when his 10th minute missile was flicked on by Jagielka himself, Dominic Calvert-Lewin attempted a header, the ball took a kindly bounce and the veteran swept the ball in with the minimum of fuss from close range.
There were Arsenal appeals for offside, and television footage seemed to show that Digne’s foot might have been over the line in the process of taking his all-important throw.
But it was certainly a dramatic intervention from Jagielka, who had only be called into the team minutes before kick-off when Michael Keane finally succumbed to a virus that had rendered him a doubt.
With his first goal in almost exactly two years, Jagielka, 36, also became the oldest goalscorer in the Premier League this season and secured a second consecutive home win against “big six” opponents - after Everton had failed to beat one of those sides in their previous 25 attempts.
But, at this stage of the season, the result was more about Arsenal shortcomings and, although they improved in attack after Emery brought on Aaron Ramsey and Pierre-Emerick Aubameyang at the interval, there was to be no salvation for the Gunners.
The pair brought about an improvement in attack, the latter’s 48th minute cross producing a weak punch from Jordan Pickford which Ramsey volleyed over from 12 yards.
But, defensively, Arsenal were even worse after the restart and the home side really should have doubled their lead on 73 minutes when a Gylfi Sigurdsson shot was charged down by Sokratis and Richarlison sliced the rebound well wide from a promising position.
The pressure seemed to be taking its toll on Emery who was involved in a furious verbal altercation with opposite number Marco Silva eight minutes from time when Skhodran Mustafi was booked for a poor foul on Richarlison as he broke clear, in front of the technical area.
“He arrived late, but I think it was a yellow card,” said Emery. “I was speaking and he (Silva) came into my space and place on the bench and explained something to me. But it was no problem.”