Jürgen Klopp apologised for Liverpool’s first Merseyside derby defeat at Everton in 14 years and admitted his team need “a crisis” to unfold at Arsenal and Manchester City to remain in the title race.

Liverpool deservedly lost at Goodison Park where Jarrad Branthwaite and Dominic Calvert-Lewin scored to give Sean Dyche’s team three precious points in their fight for Premier League survival. Everton’s victory leaves Liverpool, who are in talks to appoint Feyenoord’s Arne Slot as their new manager, trailing leaders Arsenal by three points and only one point above City, who have two games in hand. A dejected Klopp admitted Liverpool had only themselves to blame for the first Goodison derby defeat of his reign.

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“To sum up, it was not good enough,” said the Liverpool manager. “We played the game, or let it happen, what Everton wanted. They scored two goals from set pieces. The first one we somehow defended three times but in the end we put it on a plate. Branthwaite didn’t even kick the ball properly but the ball rolls over the line.

“After that we had our best period. We created big chances but didn’t score. Each situation we missed gave Everton momentum even more. Second half as well, not good enough. Then you concede the second goal. I think everybody who is with Everton saw that goal already 20 times. That’s their routine, everybody knows they put the ball there. The player is completely free. Obviously not the most inspired performance of all times. I really feel for the people, I am really sorry for that.

“We never lost here before and that feels really different. I really apologise for that. It was absolutely unnecessary but it happened. Now we have to recover because the quickest of all turnarounds is waiting for us (at West Ham at 12.30pm on Saturday). I can imagine it will be a challenge, mentally and physically.”

As for Liverpool’s chances of winning the second Premier League title of his tenure, Klopp conceded they are fading. He added: “I can’t say now that we are still fully in it. We need a crisis at Man City and Arsenal and we need to win football games because if they start losing all their games and we do what we did tonight then nothing changes. We are not safe in the Champions League [qualification] as well so we should just play better football. That would be really good.”

Liverpool captain Virgil van Dijk was scathing over the end-of-season run that has seen Klopp’s team drop points at Manchester United, Everton and at home to Crystal Palace. “Everyone has to look in the mirror and look at their own performances and ask if they really gave everything and do they really want to win the league?” said van Dijk. “We still have games after tonight but I think if we play like we did today, not winning challenges and giving the ref the opportunity to give free-kicks like we did many times, then we have no chance to win the title.”

Everton manager, Sean Dyche, was by contrast delighted with his side’s reaction to losing 6-0 at Chelsea nine days earlier. He said: “The last two games (wins over Liverpool and Nottingham Forest) have been a real forceful show of a reaction. People said we don’t care. Of course we care. How can you do my job and not care? The reaction has been fantastic from all concerned.”