The visitors took a third-minute lead at Vicente Calderon when Karim Benzema prodded Angel di Maria’s cross home, but Atletico fought back in what was a fiery encounter.
Diego Simeone's side were unlucky not be awarded several penalties as Diego Costa was brought down more than once in the box, but each time referee Carlos Delgado ruled in favour of Real.
Goals from Koke and Gabi gave Atleti a 2-1 lead at the break, but Cristiano Ronaldo netted an 82nd-minute leveller to snatch a share of the spoils - simultaneously extending Real's unbeaten run to 28 matches in all competitions and denying Atletico a first La Liga double over their neighbours in 63 years.
But afterwards, Ancelotti was more concerned with a less-than-flattering assessment of the hosts, who saw coach German Burgos sent to the stands for confronting referee Delgado in the second half.
"Atletico tried to play a violent match, not our style," said the Italian. "(Our response) was just to think only of playing and not other things.
"We must take the draw. It was a difficult game. We tried to play but it was not so easy. Our second half was very good. In the first half, after (Karim Benzema's) goal, we tried to defend high up but we let Atletico back into the game.
"Atletico had more difficulty in the second half because we moved the ball across our front line, left to right. We were not patient in the first half. They got tired in the second.
"We lost the ball too easily in the first half, that's why Atletico could get into the game."
Real defender Sergio Ramos added that he and his team-mates became complacent after taking the lead, but he was happy to earn a draw.
Ramos told Canal Plus: "Maybe after the early goal we relaxed a bit too much, but after the break we came out with more intensity.
"We've got a point, but at the end of the day we're having a great season. This is a very difficult stadium to play in.
"Our first 15 minutes were great, but then we relaxed a bit and they took their chances. After that though, we improved."
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