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And while he played down his exuberant celebration, Van Dijk clearly saw the result as a response to those who thought Liverpool might be heading for a period of struggle after their Champions League exit and defeat in the Carabao Cup final.
“It's a funny world.
There were doubts outside all of a sudden but the fact is there are eight games to go, there is a 12-point gap, and we focus on putting points on the board and playing the best football we can play,” Van Dijk said.
With Kelleher wanting a starting place, it seems certain he will leave Anfield, but when asked what advice he would give the Irishman, Van Dijk - with a reference to himself and the others out of contract - replied: “Be a Premier League champion.
We have to run, we have to out-work opponents”
While a clean sheet was again the basis of another Premier League win, the victory over Everton came courtesy of a Diogo Jota goal, his first in three months.
But Van Dijk could clearly sense it had been on its way, saying: “He came back very sharp from Portugal, was good in training, so for him it was a case of just keep going, stay important.
"We know how much work he does in order to be important and his goal was important.
His work-rate and quality on the ball was good too.”
Diogo Jota celebrating his winner against Everton(Image: PA)
As well as Jota, Van Dijk believes the international break - even though it meant a couple of games for most players - might have done his team-mates good in the wake of the Wembley defeat to Newcastle.
He said: “I liked it.
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