Jamie Carragher says Liverpool’s Premier League title hopes are over after their defeat at Everton – a result that prompted Jurgen Klopp to apologise to supporters.

Liverpool slumped to a 2-0 defeat at Goodison Park on Wednesday night – their first loss at Everton in the Premier League since 2010 – and now find themselves three points behind leaders Arsenal with four matches to play.

However, if Manchester City win their two games in hand, the champions would move five points clear of Klopp’s side – prompting Carragher to call time on their chances of winning a second Premier League title.

Speaking on Sky Sports, he said: “It’s Everton’s night. You have to give it to them. You have to accept that as a Liverpool fan.

“This is the end of the title run for Liverpool. It almost feels like the end. They just have to make sure they finish the season strongly.

“They had enough chances in the game but at the moment they are not clinical enough in both boxes.

“I don’t think you can get too angry with the team or Jurgen Klopp. It’s been a great ride and a great journey. But tonight is Everton’s night and you have to take it on the chin.”

Klopp: I can only apologise to the fans

Klopp accepted Liverpool’s performance was “not good enough” and bemoaned the way his side played into Everton’s hands, conceding both goals from set-pieces.

Speaking to Sky Sports, Klopp – who was coaching his last Merseyside derby before standing down at the end of the season – said: “I’m very disappointed.

“We let it happen to become the game Everton wanted. Two goals from set-pieces. They are really strong.

“But we created a lot and didn’t score. Then in the second half we were emotional and in a rush, not really clear enough.

“Then we concede a second goal with a routine they do the whole season – we knew the ball was going there, we just didn’t defend it well enough.

“It was free-kick after free-kick. That was part of the story. But we weren’t good enough.

“I didn’t expect that performance but it happened. It’s not the greatest moment we’re in but you have to fight through it, use your moments to get your momentum.

“We had a bit of that after Fulham but our two strikers, one is injured [Diogo Jota] and the other is a father [Cody Gakpo]. That’s not helpful.

“You don’t play your best football and are 2-0 down to a passionate, fighting opponent. We tried but it wasn’t good enough. When you win there are 500 reasons, but when you lose it’s just not good enough. That’s how it is.

“I can only apologise to everyone who is with us – it’s hard for us but I know for our people it is especially hard. We should’ve done better but we didn’t and that’s why we lost.”

Neville: Liverpool were predictable

Speaking on the Gary Neville Podcast, Neville agreed with Carragher’s view on Liverpool’s title chances, saying: “It’s going to be very difficult for them to win the league.

“It’s not over because things can happen – Brighton could somehow beat Manchester City and Arsenal could lose in the North London Derby.

“But I think they’ll go into that dressing room tonight and it’ll be a sullen atmosphere. They’ll know it’s probably gone.

“That’s where I’d be at. I can’t see them winning the title from here. It would be difficult anyway but from here? No.

“In my mind, you’d almost have to be perfect if you were Liverpool and Arsenal, and I think losing tonight is a real problem for them.”

Neville also echoed Klopp’s opinion that Liverpool were below par at Everton, saying it reflected a pattern in their recent performances.

“There were parts of their first half at Fulham that I didn’t like on Saturday,” said Neville. “I don’t like Liverpool but I like Liverpool’s style, when they play quickly and there’s a real fizz in their passing.

“They just played a little slowly from the back – a little more predictable.

“I know they’ve changed over the years under Jurgen Klopp. That first period was fast and furious, and at times a bit erratic, but I’d rather them go back to that.

“Tonight they were sloppy, they gave the ball away and free-kicks away. They missed big chances.”

Van Dijk: Season can’t end like this

Liverpool captain Virgil van Dijk urged his team-mates to question their desire to win the Premier League, telling Sky Sports: “Very disappointed in so many ways.

“I think everyone has to look in the mirror, look at their own performance and if they really gave everything. Do they really want to win the league?

“We are fighting, there are games after tonight, but play like we did overall in the game like today – not winning challenges and giving the ref an opportunity to give a free kick, like he did many times – then you have no chance to win a title.

“It’s a tough one and we need to do much better against a side that’s fighting relegation. We had clear-cut chances in the first half that we should have scored but we weren’t good enough and it starts with the fight.

“We can’t let the season go out like this.”

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