Real won 3-0 via goals from Fede Valverde, Brahim Diaz and Endrick.
Ancelotti said: "We have to be pleased with the win. We have to remember the problems we encountered, especially in the first half. We improved defensively. The rhythm of the first half was loose and slow. We were more energetic up front in the second half and had more mobility on the ball.
"The team played closer together and got the ball back quickly when we lost it. They were better defensively than in the Mallorca game. It's not just the forwards who were better; we were better as a unit today.
On Valverde's free-kick goal, Ancelotti smiled: "It's much more difficult to score from a direct free-kick in football these days. Valverde strikes it well and we have to take advantage of it. It's difficult to score from a direct free-kick because the wall jumps as well and it's very difficult. Valverde is a danger in that situation, he did very well today and he's obviously the one who has to take free kicks. I'm not going to put him under pressure.
"He is still improving, he shows a lot more character and he has a lot more responsibility in the team now. He's an irreplaceable player thanks to his quality, his strength and his intelligence. We're lucky to have him. When Kroos left the club, I think he chose the perfect player to replace him."
On Kylian Mbappé's home debut, Ancelotti said: "He's a superb forward, very quick, he has good movement off the ball, he attacks the back and he's had three or four chances that he's created with his movement.
"He's going to score in that position because he always has. He doesn't need to play on the left or centrally all the time because he's going to score a lot of goals."
And on Endrick's goal on his home debut, Ancelotti added: "He's looking very good and he has a lot of potential. He has shown his quality very quickly with his control and he's got a very powerful shot. He's a centre forward and very dangerous in tight spaces."