The Toffees have not beaten Liverpool since 2010, but go into Monday's clash at Goodison Park buoyed by victory over Arsenal in midweek.
Even by the standards of recent matches between the city rivals, the last meeting was one to forget for Everton, who lost 4-0 in April after Ramiro Funes Mori was sent off for a horror tackle on Divock Origi.
Roberto Martinez's tenure as Toffees boss ended three weeks later, with Koeman taking over in the summer.
The Dutchman said: " Of course it's not a normal match, we know about the derby rivalry between Everton and Liverpool, but my position is to prepare the team and always in these kind of derbies you have an emotional part, and that you need to control
I think it's the most important thing
"We showed last Tuesday two different faces in the game
Everybody knows which face we like to have from the start in the game and that's what we need
"The derby is all about the fans and we understand that, but we need to be calm and stay with 11 on the pitch."
Koeman is no stranger to derbies, having played for or managed the likes of Ajax, Barcelona and Benfica.
He said: " My favourite was between Barcelona and (Real) Madrid because of that rivalry between Catalonia and Madrid, and it's not only the football side, it's also a little bit the political side involved in that game
"That was really special, but I'm looking forward to being part of the Merseyside derby
Everybody told me it's a derby that everybody likes."
The victory over Arsenal came at just the right time to imbue Everton with some much-needed confidence ahead of their most eagerly-anticipated match of the season
The Toffees went into Tuesday's match on a run of only one win in 11 games and were staring at another disappointing result when Alexis Sanchez scored an early goal for the Gunners
But Everton's response, met enthusiastically by their fans, was impressive and goals from Seamus Coleman and Ashley Williams completed the turnaround
Williams' winning header came five minutes from full-time and was the third time in five matches that a late goal had earned them points after draws with Swansea and Manchester United
Koeman knows they must try to address slow starts in games, but said: " The positive side is that we keep our belief, our spirit until the end of the game to get a better result
That's part of the character of the players
"Of course we'd like to start better
Last Tuesday it was more about nerves, no confidence in the game
We made it difficult at the start, but we had a great reaction and that's how we need to play, at least at home
"We had that understanding from the fans and that makes it really tough for every opponent to win at Goodison Park
"It was a really important game - first of all the three points but also the way we played after the first 20 minutes
It was really important to know what we need to do as a team, with that positive aggression on the pitch
"It's difficult to play always like that because it's also about opponents but that spirit in the team is so important."
Source : PA