Jurgen Klopp admitted Liverpool have effectively played themselves out of the Premier League title race after defeat to Everton, and warned his side have not yet secured their place in the top-four.

The Reds were beaten 2-0 in Klopp’s final Merseyside derby, the first time they have lost at Goodison Park since 2010. The Toffees out-fought Liverpool and were a constant threat from set-pieces, with goals from Jarrad Branthwaite and Dominic Calvert-Lewin both coming from dead-ball situations.

It is a result that leaves Liverpool relying on significant favours elsewhere, trailing Arsenal by three points and with a one-point advantage over Manchester City, who have two games in hand.

The Gunners, who hammered Chelsea 5-0 on Tuesday, travel to face rivals Tottenham this weekend, while City have a potentially tricky trip to Brighton on Thursday night, but Klopp could not put a positive spin on his side’s title ambitions.

“We need them to lose games and historically they don't do that,” Klopp told Match of the Day.

“Arsenal didn't look very weak last night. We have to play better, that is it. We need points. We are not safe in the Champions League. Tottenham have played a lot of games less than us."

While Tottenham, fifth in the table, do have two games in hand over Liverpool, they trail the Reds by 14 points and still have a trip to Anfield, as well as home matches against Arsenal and City.

Liverpool made a slow start to the match at Goodison Park, with Everton only denied an early penalty after a VAR review found Calvert-Lewin was offside before he was brought down by Alisson.

The visitors conceded a regular stream of cheap free-kicks, enabling Everton to play to their strengths and keep putting the ball in the Liverpool box, where Branthwaite and James Tarkowski won almost every header.

"I'm very disappointed,” Klopp said. “We let it happen exactly the game that Everton wanted.

“Two goals from set pieces... there they are really strong. We created a lot and didn't score. I think that would have been possible in the first-half.

“In the second-half, emotions, we were in a rush, not really clear enough. And then we conceded the second goal with the routine they do all season. We knew exactly the ball would end up there, we just didn’t defend it well enough.

He added: ‘We weren't good enough, that’s what we have to admit, absolutely.”