Jude Bellingham struck a winner in injury-time as Real took charge of their Champions League round 16 playoff with this first-leg victory.
Ancelotti said afterwards: "We didn't deserve to be 1-2 down. We were really dangerous and defended really well. At the end of the day the victory is deserved. We have to stay calm. It's only the first half. Anything can happen at the Bernabeu.
"The character, the personality. We had a good block defensively. It wasn't easy. Tonight we were able to do this.
"They are a really good team and they played a really good game in my opinion. I think it was a penalty (Phil Foden fouled). The referee is one of the best in Europe."
On Bellingham, he added: "It was a big goal. He played a fantastic game and was always dangerous. It was a top game for him."