Liverpool manager Juergen Klopp apologised to fans after a 2-0 loss to Everton in the Merseyside Derby that all but extinguished their faint hopes of winning the Premier League title.

"(Leaders Arsenal and Manchester City) must have a very bad moment," Klopp, who looked completely shattered, said when asked about his team's chances.

"I don't know. I can only apologise for today (Wednesday) to the people. Everybody who's with us knows how hard this was for us as well. We should have done better but we didn't."

Jarrad Branthwaite and Dominic Calvert-Lewin scored in a 2-0 victory that will not soon be forgotten by the Everton faithful at Goodison Park, who serenaded the visitors with "You lost the league at Goodison Park" after the final whistle.

It was the Toffees' first home derby win in more than 13 years and prevented Liverpool from climbing level with Arsenal at the top of the league table.

Klopp's men are three points behind the Gunners (77) with four games remaining in the much-loved manager's tenure with the team.

"Obviously very disappointed with a lot of things. We let it happen exactly the game that Everton wanted. Two goals from set pieces. We created a lot but didn't score. We were in a rush, not really clear enough. But we were not good enough, that's what we have to admit, absolutely.

"Of course, I didn't expect that today but it happened anyway. Obviously it's not the greatest moment we are in. In the end it's not good enough. When you win you have 500 reasons. When you lose, it's just not good enough."

Klopp could only shake his head about Calvert-Lewin's 58th-minute goal from a corner kick, saying Everton have had that set piece in their play book all season and his players were prepared for it.

Liverpool captain Virgil van Dijk was blunt in his assessment, telling Sky Sports "We have to do much better. If we play like today we have no chance to consider ourselves in the title (race). It's a tough one and obviously we have to do much better against a side that is playing against relegation."

He added: "Very disappointed in so many ways and I think everyone has to look in the mirror look at their own performances, did they give everything and do they really want to win the league?"

Branthwaite is the first Everton player to score against Liverpool since Demarai Gray in a 4-1 league home loss in late-2021.