The Reds came out on top in a breathless seven-goal thriller at the Emirates Stadium thanks to Philippe Coutinho's brace, and goals from Adam Lallana and Sadio Mane, which topped off an instant Premier League classic.
But having led 4-1 at one stage, Klopp's men allowed the Gunners to score twice and restore their hopes of rescuing at least a point.
Though they failed to do so, Moreno's performance - conceding a penalty in the first-half which Simon Mignolet saved before being caught out-of-position for Theo Walcott's strike just 69 seconds later - seemed to support the idea that Liverpool require a new signing at left-back.
The position had been identified as one of the priorities going into the summer window, with Leicester City youngster Ben Chilwell thought to be Klopp's first-choice target to come in after Moreno's dire display in the defeat to Sevilla in last season's Europa League final.
But Klopp is said to have baulked at Leicester's asking price for teenager Chilwell, who has yet to make his league debut. After seeing a £7 million bid rejected, the offer consisting of £2 million in add-ons, the league champions were thought to be demanding around £10 million for the England youth international.
Klopp himself directly refused to pay as much for Chilwell and is also said to have been put off of the regularly-linked Jonas Hector of Koln because of his reported £20 million price tag.
Both left-backs have since signed new contracts at their respective clubs, removing any possibility of them moving on in the near future, leaving Liverpool in the lurch.
Klopp reluctant to spend big on new left-back as he backs himself to get the best out of Moreno
But despite the criticism of Moreno, whose positioning and rashness is frequently targeted, Klopp believes he can still improve the Spaniard and sees midfielder James Milner as the ideal competitor on the left side of defence.
Although the England international would much prefer to play in his favoured central midfield role, it's thought he would be prepared to play in an unorthodox left-back spot to meet the team's needs.
Another potential option is the versatile Joe Gomez, who hasn't played for the club in almost a year because of a serious knee injury and more recently an Achilles-related setback.
The highly-rated 19-year-old started last season at left-back before his progress was cruelly curtailed by serious injury and could feature there in the future.
However, Gomez's return to fitness is still some time away with no date yet named for when he will be back in first-team training from his current Achilles problem.
Otherwise First-choice right-back Nathaniel Clyne is capable of swapping flanks, while centre-back Ragnar Klavan can fill in there in a time of need, but both are emergency options only.
Klopp will nevertheless persist with Moreno as his only recognised left-back in the squad, provided injuries don't further deplete his options before the transfer window shuts.
Milner is likely to be the favoured starter upon his return and it is expected he would have played at Arsenal if not for injury, which he picked up in a pre-season friendly against Barcelona the previous weekend.
The news may come as disappointing to supporters, who have clamoured for a new signing at left-back since the start of the summer. Their desire for a fresh face was only renewed with Moreno's erratic display at the Emirates.
Yet, the 24-year-old still has obvious potential. It is whether Klopp can invoke sufficient improvement from the defender in certain areas of his game, which will decide whether Klopp's decision is a successful one or one he comes to regret.