Real Sociedad pipped Valencia to the fourth Champions League spot on the final day of last season, but lie six points behind them now, still without a win since the first day of the campaign.
Valencia are unbeaten in their last four games and are seventh in the table.
Nonetheless, Djukic still sees Jagoba Arrasate's side as a rival to qualify for Europe's elite competition next season, and underlined the importance of securing all three points at the Mestalla to pile further misery on them.
The Serbian told a press conference: "We want to win this game because we want to get into the Champions League spots and improve our league position.
"La Real are a direct rival and we want to put them many points behind us.
"They are strong on the counterattack and have fast players who can cause damage on the wings. But we are Valencia and when we play at home, we need to win."
Club captain Ricardo Costa has been named in Djukic's squad for the game after recovering from a knock he picked up on international duty with Portugal. Vicente Guaita will keep his place in goal with Diego Alves still injured. Helder Postiga,
who came on as a second half substitute in the 1-1 draw with Athletic Bilbao a fortnight ago after recovering from a light injury, could return to the starting line-up.
La Real defender Carlos Martinez insisted there was no need for his club to panic, despite their disappointing form which has left them 15th in the table, and said his team deserved more points at this stage.
"I don't think there's any urgency, but we need to win to change our dynamic," he told a press conference.
"It's true we aren't winning, but we haven't been awful either. We've lost many games in the last minute after being competitive in nearly every game.
"We have the feeling that we have let some triumphs slip away from us, not that we are terrible players."