Jordan Pickford held up his hands in apology to the aghast away section after gifting the 232nd Merseyside derby to Liverpool. Other Everton players lay on the pitch, stared into the middle distance or, in the case of Lucas Digne, stormed down the tunnel pushing aside every offer of consolation as he went. Liverpool’s 96th-minute winning goal had been freakish but the outcome, the pain and regret, were all-too familiar for their Merseyside rivals. Anfield remains Everton’s venue of nightmares.

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This was, as Jürgen Klopp had predicted, the Liverpool manager’s toughest assignment in a Merseyside derby and far removed from his first experience, when a 4-0 defeat of Roberto Martínez’s shambolic Everton side left him bemoaning a second half that was “no real fight any more”. This was a fight from the first minute to the 96th, when the England goalkeeper pawed a Virgil van Dijk miscue that was sailing out of play back on to his crossbar and on to the head of the grateful Divock Origi.

Origi, a potential transfer target for Everton next month, duly nodded home to send Klopp sprinting across the field of play, Liverpool back to within two points of Manchester City and their local rivals into despair. The last time Everton savoured a win in these quarters was in 1999. With errors of this magnitude and gilt-edged chances squandered, the drought seems less surprising by the year.

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Pickford started and finished the derby carelessly, slicing a routine clearance out for a corner in the opening seconds before being trapped by uncertainty at the very last, but performed well in-between with one stop from Xherdan Shaqiri particularly impressive. The in-between will be forgotten. Errors rarely escape punishment at this level and for all Everton’s improvement and Liverpool’s late fortune – “lucky, lucky, lucky Liverpool” as Marco Silva described them – the majority were served up by those in royal blue. The visible lift in their performance and adventure at Anfield offers meagre consolation in the aftermath of a defeat of this nature.

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There has been clear improvement during the first five months of Silva’s reign without the statement victory against a top-six club that would enhance his side’s confidence and make the rest of the Premier League take notice. It is a deep-rooted flaw that precedes the current Everton manager and dates so long it appears to grip the club’s psyche in the build-up to such assignments, Anfield especially.

In the past 10 years alone Everton have won only five of 64 away games against the leading pack – losing 36 and drawing 23. Their most recent victory at a so-called big six club came at Manchester United in December 2013 – their first win at Old Trafford in the past 26 years – while it has been eight years since a win at Manchester City, 10 at Tottenham, 19 at Liverpool, 22 at Arsenal and 24 at Chelsea. They will rue the hat-trick of golden first-half chances that provided opportunity to end the drought that matters most of all to their supporters, although the visitors did not monopolise the game’s brightest moments by any means.

Facebook Twitter Pinterest Marco Silva consoles Richarlison after the final whistle. Photograph: Everton FC/Everton FC via Getty Images

Silva’s side were inventive, attacked with clear purpose and quality whenever a fast-paced derby allowed, and Yerry Mina should have opened the scoring after four minutes when picked out by Digne’s free-kick. The Colombia defender was free in front of the Kop goal having escaped the attentions of Trent Alexander-Arnold but steered a clear header down and wastefully wide. Alisson produced a fine block to deny André Gomes at point-blank range, Joe Gomez an even better intervention on the goal-line from the rebound. But Gomes’s header from Theo Walcott’s invitation made it too easy for the Liverpool goalkeeper with much of the goal to aim for.

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That was a rare blemish on an otherwise classy display from the on-loan Barcelona midfielder, however. Gomes has oozed style and composure since his delayed debut against Crystal Palace in October. The Portugal international is one of several recruits made by Silva and the director of football, Marcel Brands, last summer who have brought much-needed balance to the squad and raised the overall quality of the team. His time at Barcelona has been beset by injury and criticism but Everton have provided the release and settled run the former Benfica and Valencia midfielder’s career desperately needed.

His 12-month loan does not provide a clause enabling Everton to sign him on a permanent basis but that should be a pressing priority for January. The misery of this defeat may have started to ease by then.