A run of just one win in six games pushed Koeman to the brink of the sack prior to October's international break before president Joan Laporta decided to hand him a stay of execution.
"We've won two games in a row and the sensations are good," Koeman said in a news conference on Saturday. "The Clasico is one of the most important games of the season and a chance to show that we are on the right path. The result is important, but it won't be decisive because there is still a long way to go.
"We have to play without fear. We're confident. We know what we can do and we want to show that. We are at home, we will have our fans behind us and I'm not going into the game with any fear."
Koeman has previously said his Barca team, which is in transition following the summer departures of Lionel Messi and Antoine Griezmann, is not good enough to compete for trophies this season, but he said there is nothing between his side and Madrid.
"If there is any difference between the two teams it's that they're more experienced in some areas," the Dutch coach added. "But we also have experience. They have youngsters like us, too, so it's more or less the same. I don't see a clear favourite for the game."
It will be Barca's first Clasico since Messi's departure, with the focus now falling on teenager Ansu Fati, who inherited the Argentina captain's No.10 shirt, and his battle with Madrid's young forward Vinicius Junior.
Ansu, who signed a new deal until 2027 this week, has scored twice in two games since returning from 10 months out, but Koeman said it's premature to put too much weight on the 18-year-old's shoulders.
"They [Ansu and Vinicius] are two young players with a lot to prove still," he said. "They're on the right path but I can only really talk about my player, Ansu.
"As I said in midweek, we have to give him time to fully recover from injury and to regain that match fitness that all players need. You can't think it's just about Ansu in the Clasico. He is part of a team, which is always the most important thing."
However, left-back Jordi Alba has made the squad after hurting his foot in midweek and Koeman insinuated he would start the match after "training normally" on Saturday.