Despite dramatically improving after the break, the Blancos failed to give their side the advantage after wasting clear-cut chances and, consequently, the third-tier club held on for surprising draw.
The 20-year-old attacker lamented the side's missed chances, but believes that on home turf they will get a victory in the second leg.
"They played very deep. They defended with a lot of intensity and were all tucked in at the back," he told the club's official website.
"Their players were excited and so were their fans, who had filled the ground long before kick-off. Now we have to win at the Bernabeu, there is no room for excuses, we have to win the tie."
Jese is in contention to feature on Tuesday when Carlo Ancelotti's men face Copenhagen in their final Champions League group game and he is pleased with his position in the squad hierarchy despite not having a regular starting berth.
"I'm feeling better little by little," he added. "There is a lot of competition and it is up to the coach to decide. You have to fight for a spot.
"We have already qualified for the last 16 but we are Real Madrid and we have to win every match."