At the final whistle, Jürgen Klopp gracefully doffed his cap to the pocket of Liverpool supporters singing his name but this was not a masterclass by any stretch of the imagination. At the end of a long week of air miles and freak injuries, they mustered the energy to squeak over the line, with Adrián’s calamitous error ultimately only a footnote. The keeper gave a spirited Southampton a lifeline after Sadio Mané and Roberto Firmino earned a healthy two-goal cushion. Just as a tricky afternoon on little sleep and minimal preparation seemed to have turned into a breeze, Adrián’s clearance from a nonchalant back pass by Virgil van Dijk cannoned off Danny Ings’s shin and into the back of the net.

It was a mistake fit for an end-of-season blooper reel and it had shades of Alisson’s error against Leicester City last September, another game which threatened to run away from Liverpool. It has not been a dull week for Liverpool or Adrián, who was left with an ankle “swollen like an elephant’s”, as Klopp put it, after a pitch invader ran on to join the Super Cup celebrations in Istanbul on Wednesday. Liverpool did not arrive home until 4.30am on Thursday, with the Spaniard receiving treatment on the flight home before the squad reported for their sole training session ahead of this match six and a half hours later. On Friday they boarded another flight, this time to Southampton. The travelling appeared to take its toll here, particularly in the first half, and Liverpool’s sloppiness was encapsulated by Adrián’s slip-up seven minutes from time. Nonetheless, the result was enough to take Liverpool top, after VAR denied Manchester City against Spurs.

Klopp said: “Sadio scored a fantastic goal in pretty much the last seconds of the first half and in the second half we made other big steps, controlled the game better, did a lot of good things but then minute 83 showed up on the screen and Adrián thought: ‘I played really well so I maybe I have to make the same mistake like Ali [Alisson] did’, and it kept the game a little bit open. Then they [Southampton] came up [the pitch] and Ings had a big chance and that’s normal. In that moment, I think the boys felt the tiredness. That was the moment: ‘Really? Now we have to go again.’ But we kept the result, I think we deserved the three points and I’m completely fine with that.

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“I said to [Adrián]: ‘Well done. Ali did the same. It’s a goalie thing to do at Liverpool.’ But no problem if we win the games. We played too many balls back to him in this period. I was happy with all of the stuff he did, all of the saves. The other players needed to feel more the responsibility in the buildup. You cannot give all of the balls back to him and hope the painkillers still help.”

Adrián was passed fit at 10am and it had all been going swimmingly on his first Premier League start for the club, the goalkeeper pulling off fine saves from Maya Yoshida and from his own defender Joël Matip to shut out Southampton before gifting Ings a goal against his former club.

Facebook Twitter Pinterest Adrián apologises after gifting Southampton’s Danny Ings a goal. Photograph: Will Oliver/EPA

The agonising thing for Ings and Ralph Hasenhüttl is that the substitute, who completed a £19m move this summer, should have restored parity but failed to convert Yan Valery’s cross from close range.

“Ingsy scored once but I think he could have been the big hero for us,” Hasenhüttl said. “The second chance to miss was unbelievable. We had three men in the box there at that moment but didn’t bring the ball over the line. That was really a pity, I must say. I think the guys, for what they invested today, they deserved to take one point and we didn’t. That’s tough to take, but finally we have to.”

Until Mané’s delicious, curling strike on the brink of the interval, Liverpool had huffed and puffed. The were off-colour: leggy, second-best and they looked and played like a team that only had one session to prepare for this match. Klopp, however, was adamant he was happy with the performance and insisted even two weeks’ preparation would not have made things any easier. Alex Oxlade-Chamberlain was outstanding before being replaced late on by Jordan Henderson, who was one of three players given a breather here after going the distance in Turkey in midweek. That allowed Klopp to field his fabled front three of Mané, Firmino and Mohamed Salah for the first time since lifting the Champions League trophy in Madrid.

Liverpool’s attacking trident has long been their pièce de résistance under Klopp and their ruthless streak compared with Southampton’s profligacy in front of goal – typified by Ings’s glaring miss in the dying moments – was ultimately the difference.

Che Adams’ first-half header sailed over the bar but the visitors also wasted chances, with Salah and Firmino both squandering presentable opportunities before the latter danced inside to squeeze home Liverpool’s second with 19 minutes remaining. That, though, was only the start of an oscillating finale. “The boys did an outstanding job,” Klopp said. “Let’s go home, recover and start again.”