Koeman appeared to be on the brink of losing his job earlier this month after Barca had won only once in six matches.
But club's president Joan Laporta moved to end the speculation by insisting Koeman "deserved the benefit of the doubt" and would stay as coach.
"I don't think it's possible to be under more pressure," said Koeman. "As Barcelona coach you have to take it, no problem. I know the importance of a clasico."
Asked if he still felt the backing of the club, Koeman said smiling: "I have to answer every game if that's the case. I think I am the coach of Barcelona now, tomorrow let's see. I feel supported by the club but I know everything depends on results."
Koeman is well aware of the advantage a full stadium could offer his side against their fierce rivals.
"We won two games in a row and the environment is much better. So we need the support of our fans against Real Madrid. We need a full house and we need to make our people proud.
"We are very excited and looking forward to Sunday. I told the players that they need to enjoy the environment that we will have in Camp Nou. It's not an additional pressure. We have to go out there and be fearless."
The clasico has been the stand-out club fixture over the past decade but Barca and Madrid have both been weakened by financial difficulties and key departures.
"It is still a special match," said Real coach Carlo Ancelotti. "I've lived it before and even without [Lionel] Messi and [Cristiano] Ronaldo, the feelings are the same, nothing changes.
"It's not about individuals. It's about the teams. The players come and go but there will always be Barcelona and Real Madrid."
Barca sit eighth in La Liga after winning four of their opening eight games but they are only two points behind Real.
"This game won't be decisive," added Koeman. "It will just show what kind of moment the two teams are in."
Ancelotti has never won at Camp Nou as a manager, a drought that spans five games across tenures at AC Milan, Paris Saint-Germain and his first spell at Real Madrid.
"I think the time has come," said Ancelotti.