Koeman saw his men overturn a one-goal deficit to beat Arsenal 2-1 courtesy of goals from Seamus Coleman and Ashley Williams at Goodison Park earlier this evening.
More importantly, the Toffees clinched three points in the Premier League for the first time since October.
And with a Merseyside derby to come against Liverpool on Monday (8pm), Koeman has urged his players to demonstrate the same passion they showed tonight if they are going to upset the Reds.
If we play with the passion we showed tonight we will do well
He said: "On Monday, the game against Liverpool is of course a totally different situation now we go with three points in the pocket.Â
"We know we are strong at home and still unbeaten.Â
"If we play with the passion we showed tonight we will do well.Â
Everton fan: Koeman is making Ross Barkley a "scapegoat"
"We will learn from this match, it was a great result."
Everton occupy seventh spot in the table, just a point behind sixth-placed Manchester United.