The visitors took a third-minute lead at the Vicente Calderon via a Karim Benzema tap-in, but Atletico fought back with goals towards the end of the first half with a well-taken Koke strike and a brilliant, long-distance effort from Gabi.
Diego Simeone's side were unlucky not be awarded a penalty as Diego Costa was brought down more than once in the box, but each time referee Carlos Delgado ruled in favour of Real.
Cristiano Ronaldo netted a late leveller to share the spoils, extending the Blancos' unbeaten run to 28 matches in all competitions and denying the Rojiblancos a first La Liga double over their neighbours in 63 years.
Ancelotti expressed his concern that the hosts, who saw assistant coach German Burgos sent to the stands for confronting the referee, approached the Spanish capital derby malevolently but praised Real's reaction in the second half.
"Atletico tried to play a violent match, which is not our style," the Italian told reporters. "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 went very well. In the first half, after 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 Madrid remain three points clear of Atletico in La Liga, with Barcelona expected to go one point behind the leaders should they defeat Almeria later on Sunday.