Many other managers would have dismissed Koeman before now - Craig Shakespeare and Frank de Boer provide immediate evidence to back up that assumption - but Neville does not think Everton chief Bill Kenwright wants to be in the business of hiring and firing and will remain patient with Koeman, who believes he is still the right man for the Toffees.
As they moved to the advertising hoardings, a supporter holding a child in one arm appeared to push Lopes in the head and seemed to aim a punch in the direction of the keeper.
"I think the irritation grows in the game for our players and in my opinion that was the problem by the referee", Koeman argued.
Arsenal find another one after 90 minutes when Wilshere slid the ball through to Ramsey, who placed a neat finish beyond the demoralised Pickford. Picking his spot, the boyhood Evertonian fired the ball into the top left corner from outside the area, giving Everton an unlikely lead.
Sanchez also found space in the box to fire a snap-shot from a tight angle but Jordan Pickford was on hand to make a save.
MF Sead Kolasinac, 6 - Arsenal's summer signing is having a slight dip in form after an excellent start to the season. There were boos from Everton fans, including when he decided to take off Dominic Calvert-Lewin, while Arsenal supporters sang that he was going to be "sacked in the morning". The two of them were sharp physically. However, the France international was booked late on for a late challenge on Niasse.
Everton are sitting in 18th place after nine games played. OK, I need to say Arsenal was the better team, had the better chances, but at 2-1 you can get a point. "The way we handled the situation away from home was magnificent". The goal summed up Everton's defensive performance, with the runners not tracked and not enough pressure on the man in possession.
That's five 'top' sides, not including Arsenal that are expected to fight it out for a spot in Europe's premier club competition next season.
Arsenal have a run of tough fixtures ahead, will they be able to build on Sunday's result?