There was much to encourage Nathan Jones on his Premier League bow but the form of two World Cup-bound South Americans, Uruguay’s Darwin Núñez and Brazil’s Alisson, gave Southampton’s new manager more to regret. The Liverpool pair excelled at opposite ends of the pitch to ensure Jürgen Klopp’s side signed off with a fourth successive victory in all competitions. Núñez scored twice in a fine overall display that illustrated his growing influence at Anfield while Alisson produced three superb second-half saves to quell Southampton’s attempted recovery. Roberto Firmino and Ché Adams had traded goals at the start of an entertaining contest that left Jones lamenting a passive first-half performance and a vibrant second, and Klopp the exact opposite. “It would have been easy for me not to take the game today, I only had one day to work with them, but that is not my character,” said Ralph Hasenhüttl’s newly installed replacement. “This is one of the toughest places you can start at and I learned a lot. We were really passive in the first half but I’m proud of how we reacted in the second.” Klopp sat at the back of the directors’ box – pity the poor seat in front of him – after being served with a one-match touchline ban on the eve of the game for his red card against Manchester City. The Liverpool manager was miked up to his assistants in the dugout below and had an excellent view of an incisive display from his team in the first half. “You can judge distances better and get a much better overview,” said Klopp of his temporary vantage point. “The first half was really good and the second half was not; we made a lot of mistakes.” Liverpool took an early lead after the Southampton defender Duje Caleta-Car was booked for impeding Mohamed Salah. Andy Robertson delivered the free-kick and Firmino, having peeled away from Mohamed Elyounoussi, flicked a free header over a crowded box into the far corner. The visiting goalkeeper, Gavin Bazunu, reacted to the danger far too late. For Firmino, however, it was a moment of timely joy having been left out of Brazil’s World Cup squad. Jones’ new charges were soon level courtesy of another pinpoint, inswinging free-kick. James Ward-Prowse was the provider from near the touchline. Adams read his captain’s intentions perfectly to gain a yard on Joe Gomez and Virgil van Dijk and steer an unmarked header beyond Alisson. Klopp’s annoyance at his team’s defending was obvious even while sitting in a crowd. A vibrant Liverpool response appeased him. Núñez was a tireless, intelligent outlet down the left. The Uruguay international almost created a second when racing on to Robertson’s pass and crossing low for Salah. Bazunu atoned for his earlier lapse with a point-blank save. There was little the Southampton keeper could do to prevent Núñez restoring Liverpool’s lead after his defenders squandered several opportunities to clear. Firmino retained possession and found Harvey Elliott, who floated a delightful ball over the visiting defence towards Núñez. The striker guided home a volley into the bottom corner. The summer signing from Benfica struck again when pouncing on another Robertson assist. Firmino found the full-back in space, and just onside, and the striker slid in to convert the inviting low cross towards the near post. It was Núñez’s ninth goal in 18 appearances for Liverpool and Robertson’s 53rd assist in the Premier League, equalling the record set by former Everton left back Leighton Baines. Southampton, to their credit, refused to be deflated by the timing of Liverpool’s two-goal cushion and carried a constant threat after the break. Their hopes of a comeback were dashed by the outstanding Alisson who, although newly clean-shaven, has lost none of his powers in the Liverpool goal The Brazil international prevented Elyounoussi chipping him at the near post, substitute Samuel Edozie beating him after a one-two with Adams and, most impressively, to repel a glancing header by the Southampton goalscorer from Ainsley Maitland-Niles’ cross. The second half brought the milestone of James Milner’s 600th Premier League appearance when he replaced Elliott. In doing so, the 36-year-old became only the fourth player to reach that total in the Premier League era following Gareth Barry, Ryan Giggs and Frank Lampard. “I am really proud to be around when he reached that milestone,” said Klopp. “He is an exceptional player, an exceptional person and essential to everything we achieved in the last few years.”