Everton secured their first win in a Merseyside derby at Goodison Park since 2010 to leave Liverpool's Premier League title aspirations in ruins after a 2-0 defeat on Wednesday.
Defeat leaves Jurgen Klopp's men still three points adrift of leaders Arsenal and only one point in front of defending champions Manchester City, who have two games in hand, reports AFP.
"We need a crisis at City and Arsenal and we need to win football games," said Klopp of his side's shot at the title with four games to go of his reign.
Goals from Jarrad Branthwaite and Dominic Calvert-Lewin took Everton eight points clear of the relegation zone.
The Toffees now look certain to extend their 70-year stay in the English top flight despite being deducted eight points on two charges of breaching financial rules.
Klopp had never lost on his previous eight visits to Goodison but his final taste of the Merseyside derby was a bitter one.
Hopes of a glorious goodbye for the German after a nearly nine-year tenure that has transformed the club's fortunes are fading fast.
"If we play like today we have no chance to consider ourselves in the race," said Liverpool captain Virgil van Dijk.
"I think everyone has to look in the mirror and look at their performance and if they’ve given everything. Do they really want to win the league?"
According to reports, Feyenoord boss Arne Slot is being lined up as Klopp's successor and the past few weeks have exposed weaknesses that need addressing in a huge summer for the Liverpool hierarchy.
- 'Energy, commitment' -
The Reds have won just one of their last four league games and have also bowed out of the FA Cup and Europa League in recent weeks.
Klopp made six changes after resting a number of key players for Sunday's 3-1 win at Fulham but did not get the response he desired.
Buoyed by their weekend win over Nottingham Forest to pull clear of the relegation zone, Everton are a side transformed from the one that went 13 Premier League games without a win between December and April.
"Delighted with the performance of our players and delighted for the Evertonians," said Everton boss Sean Dyche.
"They're a good side, we know that. The commitment and energy from us had to be there."
Slow starts have been a recurring factor as Liverpool's quest for four trophies has unravelled.
Everton thought they had a penalty in the opening minutes when Calvert-Lewin was tripped by Alisson Becker but VAR intervened to save the visitors as the striker was offside.
Alisson then clawed away a Calvert-Lewin header and Ben Godfrey nodded wide as Liverpool struggled to cope with Everton's threat from set-pieces.
More comical defending from the Reds led to the opener on 27 minutes.
Alexis Mac Allister's mishit fell perfectly for Branthwaite and the defender's effort went in off the post despite Alisson's best efforts.
Going behind woke Liverpool from their slumber and only a combination of wasteful finishing and Jordan Pickford preserved Everton's lead until half-time.
Darwin Nunez blasted straight at the England number one when clean through before the Uruguayan teed up Luis Diaz to fire too close to Pickford.
Mohamed Salah's loss of form has come at the worst possible time for Liverpool's title challenge and the Egyptian sliced another good opening well over the bar.
Liverpool were camped in the Everton half after the break, yet the hosts pulled further clear just before the hour mark from another dead ball.
Calvert-Lewin was afforded a free header at the back post to power home Dwight McNeil's corner.
Liverpool's night was summed up when Diaz's powerful effort came back of the post with Pickford finally beaten.
But it was Klopp who was crestfallen come the final whistle as he looks set to depart Anfield with just one Premier League title to his name.