Jamie Carragher believes defeat to Everton “is the end” of Liverpool’s hopes of winning the Premier League title in Jurgen Klopp’s final season at the club.

Liverpool were beaten 2-0 at Goodison Park in the Merseyside derby as goals from Jarrad Branthwaite and Dominic Calvert-Lewin proved too much for the visitors.

Branthwaite opened the scoring in the first half, tapping the ball in at the near post after Liverpool failed to clear.

After the break, Calvert-Lewin headed the ball powerfully into the back of the net, and his physical presence caused a problem for the Reds all night.

Liverpool are three points behind leaders Arsenal in the title race, while Manchester City can go five points clear if they win their two games in hand.

Former Liverpool defender Carragher said to Sky Sports after the match: “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 are not clinical enough in both boxes.”

He added: “Tonight is Everton’s night, you have to take it on the chin.”

While Liverpool still have a small chance at the title, captain Virgil van Dijk said the Reds have “no chance” of winning the Premier League if they play like they did at Goodison.

“Very disappointed in so many ways,” Van Dijk told Sky Sports. “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.”

Liverpool missed out on a chance to go level on points with league leaders Arsenal, but instead will go into the final four matches of the season three points behind, and with Manchester City having a game in hand.

The result gave Everton’s chances of staying in the top flight a massive boost, although without the eight-point deduction they would have already been assured of safety.

It was only Everton’s second Merseyside derby victory in the Premier League since 2011, and it was one that will mean a lot to the club as the players and fans celebrated following the final whistle.