Roberto De Zerbi praised his Brighton predecessor, Graham Potter, for bequeathing him a great team and said: “I tried not to damage it.”

The mission statement was the only modest aspect of the Italian’s Premier League debut as Brighton became the latest side to prey on Liverpool’s defensive vulnerabilities.

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Leandro Trossard launched the De Zerbi era in style with the first hat-trick by a visiting player at Anfield since Andrey Arshavin struck four for Arsenal in 2009. Liverpool fought back from two goals down to lead through a Roberto Firmino brace and an unfortunate own goal from Adam Webster but victory would have flattered Jürgen Klopp’s team. “I wasn’t 100% convinced we wouldn’t concede at 3-2,” the Liverpool manager admitted. Trossard proved him correct seven minutes from time.

It was the least the visitors deserved and the fifth time Liverpool had dropped points in seven league games this season. Klopp was visibly deflated by their inconsistency.

De Zerbi had wanted brave football and that is exactly what he got. The confident visitors were prepared to play through Liverpool’s press inside their own penalty area and thread inch-perfect passes through central midfield, and shredded the home defence repeatedly as a result. But for a brilliant save by Alisson and a poor header from Danny Welbeck they would have been four goals ahead inside the opening 18 minutes and cruising before Firmino changed the complexion of the game. Klopp admitted Liverpool were surprised by Brighton’s formation and approach. It took an age for them to react.

The breakthrough arrived early and following a weak clearance by Trent Alexander-Arnold. Having issued a staunch defence of the Liverpool right-back after he was dropped by the England manager, Gareth Southgate, Klopp could have done with a convincing response from a talent he described as “world class”. It was not forthcoming, with Alexander-Arnold erring for both Brighton goals and almost for a third on the stroke of half-time.

After the defender headed a Solly March cross back across the Liverpool area the excellent Moisés Caicedo beat Jordan Henderson to the second ball and found Alexis Mac Allister. His touch was back-heeled by Welbeck to Trossard, who slipped away with ease from Alexander-Arnold and drove into the far corner.

The Liverpool defence was torn apart in the early stages. Another March cross picked out Welbeck unmarked in the centre of Liverpool’s goal. Six yards out, and with Alisson exposed, the centre-forward headed straight at the Brazil international when he had to do better.

Alisson came to the home side’s rescue following a careless mistake from Thiago Alcântara, who allowed the goalkeeper’s throw to roll under his foot to Pascal Gross. Suddenly Welbeck was free inside the area. His touch fell to Trossard whose shot was destined for the bottom corner until Alisson stretched out a leg to save with his right foot. It was a vital intervention, although Liverpool’s afternoon would deteriorate before the rescue act commenced.

Brighton deservedly doubled their advantage when Alexander-Arnold chested a long ball into the path of Welbeck. Pervis Estupiñán sent the striker scurrying down the left and he squared to March, who released Trossard with a lovely first touch. From a similar position to his first goal, the Belgian forward swept another sharp finish beyond Alisson.

When Virgil van Dijk prevented Welbeck pouncing on another flowing Brighton move Liverpool were floundering badly, struggling to contain the visitors’ adventure or retain possession long enough to threaten a response. But the comeback commenced courtesy of a much-needed intervention by VAR.

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Firmino’s finish was initially disallowed for offside by the referee, Andrew Madley, after a flag from his assistant when Mohamed Salah had latched on to Henderson’s chip and turned the ball into the path of the Brazilian striker. VAR, however, ruled that Webster had played Salah onside when the captain’s ball sailed over the top and, after a lengthy deliberation, Madley overturned his decision to the unrestrained joy – and relief – of Klopp.

The Liverpool manager introduced Luis Díaz for Fábio Carvalho at half-time and the switch paid dividends when the Colombian winger helped create the equaliser. After a Brighton break floundered Henderson sprayed a fine ball out to Thiago who released Díaz into a one-v-one against Joël Veltman. He centred to Firmino, who breezed away from Lewis Dunk before beating Robert Sánchez with a cool finish.

Liverpool overturned their two-goal deficit in bizarre fashion when the Brighton goalkeeper made a mess of attempting to punch clear an Alexander-Arnold corner. The ball sailed past Sánchez’s fist and struck the unfortunate Webster before bobbling over the line.

The comeback was on but built on suspect foundations with Liverpool’s defence continually vulnerable against Brighton’s probing runs. Kaoru Mitoma produced a lively display as a second-half substitute. His cross from the byline should have been cut out by Van Dijk but it sailed past the defender to Trossard at the back post. The hat-trick was sealed with an emphatic shot that Alisson could only push into the roof of the net. The only damage De Zerbi inflicted was on Liverpool.