Goals from Sadio Mane, Philippe Coutinho and Divock Origi helped Klopp’s team to a convincing victory at Anfield which strengthened their hopes of securing Champions League football next season.
Matthew Pennington’s first goal for Everton in front of the Kop briefly restored parity, but Liverpool were far too strong and ran out comprehensive winners.
An injury-time goal from Mane ensured a 1-0 win over their local rivals earlier this season, while Klopp also masterminded a 4-0 win over the Toffees in his first Merseyside derby just over a year ago.
“The boys did everything they could to show the power of Anfield, I think it was well deserved,” said Klopp.
“We played good football and we coped well. They tried to play the system which they played against Man City, when they won 4-0, that’s the first sign of respect.
“We had to defend at the end and our organisation was not that good, but we defended with passion and could have had one or two more clear counter attacks, but all good.
“Under the circumstances it was a really good game and we did the job we had to do.”
It was not all good news for the Reds as Klopp confirmed that Sadio Mane is set to miss the game against Bournemouth on Wednesday due to injury.
“When I saw him (Sane) in the dressing room, it didn’t look like he’ll be ready for Wednesday.
“We will see, hopefully it’s not that serious, but of course it’s not nothing and that makes our life not easier, I would say.
“Obviously he has pain and it didn’t look like it’s only a knock or a muscle or something, but we have to wait.
“When I came in I was looking for him immediately and I saw him on the bed. He’d already had treatment, and it didn’t look like he felt really comfortable.
Liverpool’s win extended their lengthy unbeaten run against Everton who have not beaten their neighbours from across Stanley Park in 13 matches and remain without a win at Anfield since 1999.