Virgil van Dijk hailed Liverpool’s record-breakers as they tightened their grip on the title with a majestic Mersey derby display.
The Reds rewrote the history books by extending their top-flight unbeaten run to 32 matches - beating the previous record set by the champions of 1987-88.
And they produced a stunning first-half blitz against hapless Everton without the rested Mo Salah, Roberto Firmino, skipper Jordan Henderson and Alex Oxlade-Chamberlain, and the suspended keeper Alisson.
The win sent Blues boss Marco Silva a step closer to what looks like his inevitable dismissal, but Van Dijk reserved praise for new-look Liverpool , with stand-in Divock Origi scoring twice, and Xherdan Shaqiri also netting on his first start of the season.
It was a stunning result for manager Jurgen Klopp, who gambled on rotating his players with a massive December programme coming up.
And Van Dijk said: "The players coming in were fantastic, it's good to see. We will need everyone in this long season.
“We have to use everyone and they all stepped up. Divock Origi was fantastic. A club record is great but we have won nothing yet, we want to go all the way."
The first half was remarkable, as Liverpool scored four - their most since 1935 in the first half of a derby - and Everton replied with two of their own to make it the most goals in a half in the derby ever.
But Everton’s defensive shambles in the first period, and their listless, unambitious display after the break surely ring the death knell for Silva. It is the first time they have conceded five in the derby since 1982.
Silva was given two games by owner Farhad Moshiri, and lost both - to Leicester at the weekend and now a derby humiliation, to plunge the Blues into the relegation zone and deep into trouble.
But defender Mason Holgate insisted the players must take responsibility for a performance that wasn’t good enough.
"We have to take pretty much all of the responsibility. The manager has told us what we need to be doing and we have not done that,” he said.
“It’s not acceptable where we are now. And we know that. We played well in patches of the game but route one balls are things we should be dealing with and we have not done that. We deserved nothing from it.”
Sadio Mane was the hero for Liverpool, and goalscoring hero Origi also starred. Afterwards, he insisted he had repaid the faith of Klopp.
"The manager showed trust in me and I tried to repay it. It was an important game, a special game,” he said.
"One of our weapons is to go in behind and I had some wonderful service. We know we have a great team and we have to be at our best. Each individual is important."