Liverpool have made the start to the season they wanted even if they have yet to hit the giddy heights of the latter part of the last campaign.

Jürgen Klopp named an unchanged side for the third time in three matches and watched his players collect a third win, moving to the top of the Premier League in the process. Klopp has been there before, though it was almost two years ago and only a brief visit. In each of his three previous seasons in England the German has had to witness teams either running away with the league (Manchester City and Chelsea) or proving uncatchable (Leicester City). This time Liverpool are understandably keen to be the ones staying a step ahead, and though there is a long way to go they are setting the pace, with some room left for improvement.

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Pep Guardiola has just claimed his Manchester City side are below maximum efficiency after a World Cup summer, and the same appears to be true of Liverpool, who put several passes astray and made too many poor decisions in the final third for their manager to be completely happy. Or perhaps they simply found an organised Brighton side difficult to break down. There was never much doubt about the result once the home side had taken a first-half lead, but Brighton were by no means overwhelmed and will kick themselves over the lapse of concentration that ended up costing them the game.

“We gave away a very poor goal but I was proud of the way we played after that,” Chris Hughton said. “We put ourselves in a great position to get something, in fact I’m a little disappointed that we didn’t.”

Liverpool could have gone in front as early as the fifth minute after Sadio Mané played Mohamed Salah into space behind Gaëtan Bong and moved into the penalty area to accept the return pass, only to sidefoot narrowly wide of goal. Brighton set themselves up to contain, Hughton revealing special measures were necessary against a team of Liverpool’s firepower, but quickly discovered that the problem with five men across midfield and only Glenn Murray as a token outlet was that it made it hard to break out of their own half. Liverpool just kept swarming forward and it took a good one-handed stop from Mat Ryan to keep out a Roberto Firmino header from Andy Robertson’s cross.

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For all that the home side had a let-off when Alisson came out of his area to deal with a ball from Yves Bissouma and failed to make any contact. Solly March was left in possession near the corner flag with the goalkeeper stranded but he miscontrolled to let the ball run harmlessly dead. Trent Alexander-Arnold hit the bar with a free-kick after Naby Keïta was fouled on the edge of the area before, almost inevitably, Salah struck midway through the first half.

The visitors will not enjoy the inquest at the training ground. From a Brighton free-kick in their own half a mixture of careless passing and Liverpool’s determined press left Bissouma caught in possession by James Milner. Mané lost no time in transferring the ball to Firmino, whose precise pass in turn allowed Salah the space to find Ryan’s bottom corner with a confident left-foot finish.

Brighton opened the second half with a chance to equalise when Anthony Knockaert shot wide. Liverpool’s inability to put the game out of reach encouraged their visitors to get forward, without producing much in the way of end-product. Liverpool’s best chance of a second goal came through their two full-backs. When Robertson thoughtfully turned the ball back Alexander-Arnold saw his effort deflected past a post.

It is probably just as well Liverpool can take solace from the league table, for they might have been embarrassed late on when Alisson had to make virtually his only save of the game to keep out Pascal Gross’s header.

“We had a good mindset in the first half but we didn’t show the same patience in the second,” Klopp said. “I wouldn’t say we were under pressure but Brighton had their moments. Alisson had to make a big save at the end but there is no need to be negative about nine points from three games.”