Jurgen Klopp said Liverpool need a "crisis" at Arsenal and Manchester City to revive their Premier League title hopes after a 2-0 defeat in the Merseyside derby at Everton left his side three points off top spot with four games left to play.

Goals by Jarrad Branthwaite and Dominic Calvert-Lewin sealed Everton's first home derby win since 2010 and all but ended fears of relegation by moving them eight points clear of the bottom three.

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The Everton supporters taunted their rivals by singing "You lost the league at Goodison Park" and Klopp, who will step down as Liverpool manager at the end of the season, said his side were now struggling to stay alive in the title race.

"I don't know why I need to answer the question, but I know how it works," Klopp said. "You can see the table. We need a crisis at Arsenal and City, so they need to not win games as we haven't done tonight. Arsenal and City must have a very bad moment.

"I can only apologise for today to the people. We should have done better but we didn't. Our performance wasn't good enough and I am very disappointed.

"We defended the first goal three times and handed it to Everton on a plate and the second goal could probably have been defended better.

"And for us, each miss gave Everton more momentum. We never had it, but we gave them more."

Klopp added that his would have to recover physically and mentally, but that the second part is difficult when you lose a game like this.

"West Ham will probably be waiting for us [on Saturday] and rubbing their hands, hoping that we turn up on one leg, but we have to recover for that," Klopp said.

Everton's victory was greeted with raucous celebrations by the home fans, who remained in Goodison Park to sing and applaud their players long after the final whistle. And manager Sean Dyche said that victory was for the supporters who have endured a season of negativity following two separate points deductions by the Premier League.

"That win is for the people," Dyche said. "We should be on 41 points and the story's different. But thats now three clean sheets in three home games. The challenge for the players is to go and do it again.

"We spoke about the desire and the energy of the team and the physical side of the game. The lads did it on Sunday and they'll have to do it again. That's the challenge."