Jurgen Klopp said Liverpool's 3-1 win over Everton was "well deserved" and refused to be drawn into a war of words with Ronald Koeman.
Sadio Mane, Philippe Coutinho and Divock Origi scored as Liverpool extended their unbeaten run against Everton in the Premier League to 13 matches.
Matthew Pennington equalised for Everton after Mane's early opener, but otherwise the hosts largely controlled the game.
"The boys did everything they could to show the power of Anfield, I think it was well deserved," said Klopp, who is the first Liverpool manager to win his first three league derbies.
"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."
One of the flashpoints in the game came before half-time when Ross Barkley was shown a yellow card for a high tackle on Dejan Lovren.
The Liverpool bench appeared aggrieved that Barkley was not shown red, with Koeman saying their reaction was "crazy".
But Reds boss Klopp was careful to watch his words regarding the challenge, saying: "I don't like creating stories.
"Our responsibility is to cool things down as much as possible. It's not easy during the game so we shout at each other and all that stuff, but after the game it's done.
"If you saw two harsh challenges then say it, if not don't use me to say it. The ref decided in different situations again."
Klopp also confirmed that Sadio Mane is set to miss the game against Bournemouth on Wednesday due to injury.
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