After Conor Gallagher struck for Atleti in the first minute, the Champions League round of 16 second-leg went to penalties with the aggregate score locked at 2-2 after extra-time.
The key moment in the shootout was a slip by Julian Alvarez, who was deemed to have touched the ball twice by VAR as he converted. As such, the penalty was ruled out.
Ancelotti said afterwards: "It was a difficult game, and even more so when you concede inside a minute. After that they dropped in to defend and looked to catch us out on the counter. The priority was to have effective possession of the ball and not complicate the game again. It was an evenly-matched tie and Atlético are one of the best in the world defensively.
"They're well drilled, defend and work hard for each other, and we had a great chance through that incredible Mbappé move but we missed the penalty and it was level until the shootout. That's when we sent our best taker up first, and then Rüdiger went last because he scored against City.
“I tried to explain our priority, which was not to complicate things by losing the ball in bad areas where they could catch you out of position. If they had made it 2-0, the game would have been very tough.
"We were better in that sense in the second half of extra-time. We always have to look to improve and work towards that. I've already explained what our approach was in this match. It looked like we needed to score a goal and we were never out of the tie at any point."
On the tension of a shootout, the Italian also said: “I have no idea what can make a difference in a penalty shootout. You have to pick the calmest guys you can. It's a lottery and it went our way. Atlético go out of the competition with their heads held high because they played at their very best. I was pretty calm about it all. When it's a lottery like that, you toss the coin and luckily it went our way."
Ancelotti also said of Alvarez's penalty denial: “I think the referees had already spotted it on VAR when we realised. I didn't see it initially, but it looks like he did touch it with his left foot when I watched it back."