The Kop boss saw goals by Sadio Mane, Philippe Coutinho and substitute Divock Origi ensure victory in the 228 Merseyside derby to strengthen the Reds’ grip on a top-four place.
But after seeing Mane limp off with a knee injury that puts him in doubt for the visit of Bournemouth on Wednesday night, Klopp told the Anfield fans not to get carried away.
The German tapped his watch towards the end of the game to tell Liverpool’s supporters that it was too early to celebrate when they began to chant his name.
And he said: “People think I am crazy because I look like this and I am really emotional.
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Jurgen Klopp speaks after win over Everton
“But I thought that when the crowd sang my name with five or six minutes left, I saw it as a sign that they thought it was done. Football isn’t done until the final minute.
“So far we have played a really good season but it isn’t finished yet.
“It was almost perfect – but then we lost Sadio Mane and it doesn’t look like he will be ready for Wednesday.
“So we will need every voice inside Anfield to help us create another good performance.”
Everton looked like they would make a game of it when young defender Matthew Pennington cancelled out Mane’s early opener.
But Coutinho’s sensational strike soon put Liverpool back in the ascendancy – and the Brazilian they set up substitute Origi for the killer third goal.
Klopp said: “Phil’s goal was so important after the equaliser. I must send a big thank-you to the Brazilian national team because he came back here in a great mood.
“It was a fantastic goal, a great finish. He wasn’t happy when I took him off but we had already lost an offensive player so I thought it made sense.”
Everton still haven’t won at Anfield since 1999. But boss Ronald Koeman said: “We played in a way I like to see Everton play. That’s why I’m proud.”