Goals from Roberto Firmino and Mohamed Salah inspired Liverpool to bounce back from a disastrous start but a penalty miss by the former just before the interval proved costly.
Put simply, any success in Europe, or domestically for that matter, this season will be determined by Klopp’s ability to bolster his chronically susceptible defence and coach them into some form of cohesion.
That was sorely absent on 72 minutes when substitute Luis Muriel played in Joaquin Correa — both players allowed far too much space —and the midfielder lifted in a perfect finish for the fourth and final goal of the evening.
Liverpool’s frustrations grew as deep in injury-time as youngster Joe Gomez collecting a second yellow card. It was a bizarre finale, especially after Sevilla coach Eduardo Berizzo had been sent to the stands on the hour after throwing the ball away from Gomez as he rushed to take a throw-in.
At that stage, Liverpool led 2-1 and, even allowing for the penalty miss, Klopp looked on course for an opening night victory even without Philippe Coutinho, whom he kept on the bench until the final desperate 15 minutes.
Anfield was in jubilant mood as the English club welcomed Champions League football back to their ground after a two-year absence but it took Sevilla just four minutes to dampen the enthusiasm.
The opening goal was the product of a poor defensive mistake by Dejan Lovren who completely miskicked while trying to clear a cross from Sergio Escudero at his near post. The defender allowed the ball to run across the face of goal where Wissam Ben Yedder had the simple task of sliding the ball into an open net.
Following on from the weekend five-goal defeat at Manchester City, it was the worst possible start for Klopp’s side, although their attacking play was promising. Emre Can had curled a shot directly at goalkeeper Sergio Rico inside the opening minute and, after going behind, Georginio Wijnaldum’s long-range effort was deflected wide. Sadio Mane came closer still, after Salah picked him out from the right-hand by-line, as his shot was saved low down by Rico, at the expense of a corner.
Jordan Henderson took that set-piece and picked out Firmino whose strong header just cleared the Sevilla bar.
But Liverpool forward Firmino needed no second invitation on 21 minutes when he equalised for his side following an incisive attack and a Henderson pass which sent Alberto Moreno away down the left.
He crossed low into the six-yard box where Firmino lunged ahead of Gabriel Mercado to turn in the equaliser.
Minutes later, the Reds should have been in front after a blistering counter-attack ended with Mane playing Can clean through on goal only for the German international to roll his shot agonising inches beyond the right-hand post..
Yet there were still moments of major concern for the home supporters, specifically, whenever the ball entered their penalty area. Before the equaliser, it had taken the combined efforts of Moreno and Lovren to stop Ben Yedder as he appeared ready to wriggle through clean on goal.
And with Simon Mignolet again “rested” by Klopp, German goalkeeper Loris Karius, and his distinctly suspect kicking abilities, were never far from those supporters’ thoughts.
Jesus Navas, rejected by Manchester City after failing to make an impact across England’s north-west, was also enjoying his return to England and left two defenders in his wake in the area on one particularly breezy run.
But, fortunately for the hosts, Liverpool’s attacking play was better than their defending was poor, even if the second goal, on 36 minutes was down to a large slice of luck and even larger deflection. Salah’s attack broke down in the Sevilla box but the winger showed great persistence and won the ball back from another ex-Premier League star Steven N’Zonzi —illegally, according to the Spaniards. The Egyptian did not hesitate, however, and unleashed a first-time shot from 25 yards with the ball deflecting cruelly off Kjaer and looping over the prone goalkeeper into the Sevilla net.
Before the interval, the game should have been well and truly over after defender Guido Pizarro first appeared to handle and then, undoubtedly did, trip Mane inside the Sevilla area, presenting Firmino with the penalty to end the contest.
The Brazilian’s shot beat Rico but not the right-hand post as it bounced off the woodwork and flew to safety.
Still, Liverpool were in no mood to let the Spaniards off the hook and, before the half-time whistle, there was still time for yet another counter-attack, this one ending with a stinging Moreno strike which Rico, this time, kept out.
Liverpool continued to press the visitors after the restart and, after Berizzo’s dismissal, Mane shot just over from the edge of the area and a Wijnaldum shot was well saved by the unsighted Rico through a crowded penalty area.
But not even the introduction of Countinho for the closing stages could produce the third goal Liverpool so desperately needed although, not for the first time this season, what they were more in need of was some quality defending.
Karius 6; Gomez 5, Matip 6, Lovren 5, Moreno 7; Henderson 6, Wijnaldum 7, Can 7 (Coutinho 75, 6); Salah 9 (Oxlade-Chamberlain 88), Firmino 7, Mane 7 (Sturridge 83). Subs: Mignolet, Milner, Klavan, Robertson.
Rico 6; Mercado 5, Pareja 5 (Krohn-Dehli 45, 6), Kjaer 5, Escudero 6; Pizarro 7, N’Zonzi 7; Navas 7 (Corchia 82), Banega 6, Correa 8; Ben Yedder 7 (Muriel 68, 6). Subs: Soria, Carrizo, Sarabia, Vazquez.