With four games left, Liverpool are now hoping for slip-ups from leaders Arsenal, who lie three points clear, and champions Manchester City.

Defeat at Goodison Park was their second in three games as their season threatens to peter out.

"Do they really want to win the league?" asked Van Dijk.

Goals in each half from defender Jarrad Branthwaite and striker Dominic Calvert-Lewin set the Toffees on their way to their first home victory in the league over Liverpool since October 2010.

It was another setback after being beaten 1-0 at home by Crystal Palace 10 days ago as they missed the opportunity to go back level on points with the Gunners.

A scathing Van Dijk told Sky Sports: "If you play like this overall in the game and not win any challenges and give the referee an opportunity to give a free-kick away then we have no chance to win the title.

"Very disappointed in so many ways. Everyone has to look in the mirror and look at their own performance and think if they gave everything.

"It is a tough one and obviously we have to do better against a side near the relegation [positions].

"If you play like today we have no chance to consider ourselves in the title race."

Van Dijk mentioned Liverpool's next game being an early kick-off at West Ham on Saturday.

Former Everton and England striker Wayne Rooney, a studio guest for Sky's match coverage, said: “The worrying thing there is – and I think it’s happened a lot throughout the season as well – again we are hearing about 12:30 kick-offs after he’s just lost a derby.

“He should be wanting, and that Liverpool team should be wanting, to be on the pitch tomorrow morning to get the next game going, because when you lose, especially in a derby, you want the next game to come quick.

“We’ve heard it so many times this season with Liverpool about 12:30 kick-offs. Get on with it. That’s part of your job. He should be ready to play.”