Klopp's men are second in the Premier League table, level on 74 points with Arsenal -- who host Chelsea on Tuesday -- and one clear of defending champions Manchester City.
Liverpool returned to winning ways at the weekend, beating Fulham 3-1 after a draw against Manchester United and a costly defeat at home to Crystal Palace.
"I don't know when my first derby was but I always knew how important it was," said Klopp. "Now I know it and I feel it. My understanding has developed over the years but they are always difficult games, especially there."
He added: "Derby fever will be in minds so we have to be cool and that is an important part in preparing for the game."
Everton have a respectable recent record against their city rivals at their own ground, losing only once there in the Premier League since 2016.
Klopp, in his final season at Anfield, said he was happy with the way his team had responded after their recent setbacks, which included exits from the FA Cup and the Europa League.
"It was super-important to qualify for the Champions League," he said. "That was clear to go for that. It looks good in that department but it is not 100 percent set yet.
"We are where we are and want to win all the games. You have to deal with all the little setbacks. I wouldn't say it was straightforward but until two weeks ago it was better than people would have thought.
"It's all about how you can get the right feeling back again. And I am really happy with the response.
"Let's make the best of it. If we win the league then I will be ecstatic. And as long as there's that chance we will give it a good try."
The German also said Portugal international Diogo Jota would be out for about two weeks after picking up an injury at Fulham.
Relegation fears
Everton's relegation fears have been eased after two wins in their past three games.
They are now five points clear of the drop zone despite being docked a total of eight points this season for breaches of Premier League financial rules.
Everton boss Sean Dyche said he was looking forward to his first Merseyside derby at Goodison Park.
"I didn't grow up here so I don't have the depth of understanding (of the rivalry) but what I do understand is how important it is to be Everton's manager in all games, but particularly this one for the obvious reasons," he said.
Speaking about Klopp's final derby, he added: "Aside from being Everton's manager, massive respect for what he's done here and his other clubs. It's not easy to build things, and he's done it at three clubs. Massive respect for that."
