This was a very frustrating loss for Everton in the end, who had produced a really stubborn and resilient away-day effort against the best side in the league and could actually have possibly won it had they converted their first-half chances.
That issue has plagued this Toffees team all season long, and once more, Dwight McNeil and Beto, who both had excellent opportunities, were not able to find the back of the net.
David Moyes has to do all he can to resolve this problem in the upcoming summer transfer window, and as has been said so often, finding a striker who is able to consistently score goals will make a decisive difference in Everton's future results and potential ceiling.
Those results have been much improved since Moyes returned to Merseyside (despite some questions over tactics and team selection and a few worrying wobbles at home), and bringing the veteran Scot back has proved overall to be a good decision by the Friedkins since they took control of the club.
Particularly on their travels during this campaign, the Blues have been excellent, with only Chelsea and Saturday's opponents, Arsenal, having a better record away from home.
Once again this weekend, Everton were superbly organised and defiant defensively, giving the Gunners probably their toughest test at the Emirates all season so far.
And this was despite the fact that the Toffees were missing their first-choice centre-back pairing of James Tarkowski and Jarrad Branthwaite, with Michael Keane and Jake O'Brien filling in very well.
Moyes has built a firm foundation for the future with one of the Premier League's best defences and a unit that seems a lot more consistently reliable than most in the league.
Last summer, Moyes set about trying to solve the team's lack of attacking and creative players to add much-needed additional goal threat.
Some progress has been made here with signings such as Thierno Barry, who has shown glimpses of potential and Jack Grealish, although he may return to Manchester City after his injury, and perhaps most effectively of all, Kiernan Dewsbury-Hall.
So, going to Arsenal, the likely champions in waiting, and producing a display that was good enough to possibly secure a point or even win it, represents a significant step up in the team's level.
Qualifying for Europe next season is still a possibility, given how tightly contested and fluid the Premier League is, and with the other sides above Everton also dropping points this weekend as well.
That would represent a major breakthrough for the club and could certainly help the Blues attract more and better talent this summer and kick on from here.
However, even if the club is not able to secure a place in European football this campaign has surely provided a basis for genuine and hopefully lasting optimism for the next few years ahead.