Real ran out 2-0 winners at the Santiago Bernabeu, courtesy of a Gareth Bale first half double - but the UEFA Champions League holders were unable to add to their lead in the second half.
Ancelotti said improvement was necessary ahead of their crucial clash against Barcelona at Camp Nou on March 22, with the Catalan club one point ahead in the title race.
"We were brimming with confidence in the first half. The second half worries me a little bit," Ancelotti said post-match.
"It is going to be a different match compared with tonight's. We need to be at our best, at our best we can win."
"The important thing was confirming that Modric and Sergio were indeed fit," he said.
"We avoided picking up any bookings for Isco and [Toni] Kroos.
"We will travel to the Camp Nou with almost a complete squad available."
"Yes, it is pretty clear for everyone. There won't be any surprises. As long as I don't lose my mind this week, there won't be any surprises," he said.
Aiding Real's chances of winning in Barcelona on Sunday will be their opponents' quick turnaround from a Champions League tie with Manchester City on Wednesday.
On Barca's shortened preparation for El Clasico, Ancelotti added: "We have the chance to train well for the whole week and prepare for the match both physically and tactically.
"It is an advantage but Barcelona are well used to playing every three days without it causing them problems."
