Los Blancos claimed a healthy 2-0 advantage over the Blues at the Santiago Bernabeu on Wednesday.
Karim Benzema and substitute Marco Asensio scored for the hosts either side of half time while the visitors had Ben Chilwell sent off for a professional foul on Rodrygo Goes.
The second leg of the tie takes place at Stamford Bridge next Tuesday, with whoever advances meeting Manchester City or Bayern Munich in the last four.
Speaking to BT Sport after the game, Ancelotti was satisfied with the result but warned of the threat Chelsea could pose at their own backyard.
"Don't forget that Chelsea are a good team with good players. We won 2-0 and took advantage of this game. It is not done yet. We need to fight and sacrifice at Stamford Bridge. This is normal, it is the quarter-final of the Champions League. We are satisfied for the game. It was a good game and we need to be ready for the next one," he said.
"When we played against 10 men they put in a low block and it was not easy to find a solution. We spent a lot of energy in the game to press high. At the end, we were not so fresh to find a solution. But the result and performance were good.
"I know football really well. My players understand there is another 90 minutes to play. It will be difficult and we have to be ready.
"I have good memories of Frank Lampard. A fantastic player. I hope for them, he will be a fantastic manager. Not necessarily on Tuesday!"
