Real are second in the LaLiga standings on 52 points, seven behind leaders Barcelona. If Barcelona, who will face Almeria on Sunday, manage a win, they could extend their lead to 10 points. Atletico are fourth on 42 points.
“I see (winning) the league as a very difficult task. It was before today’s game and now it’s got even tougher,” Real manager Carlo Ancelotti told DAZN.
“Today we lacked a bit of mental freshness, more than physical. Especially when they were down to 10 men, we allowed them to score and struggled to reposition ourselves.
“In the first half we had good control but the intensity was not high. Then we didn’t take advantage of the extra man we had.”
The match started slowly on a freezing afternoon, with light snow falling on the Spanish capital and Real Madrid dominating play but unable to turn their numerical superiority into scoring opportunities.
Karim Benzema, Vinicius Jr and Marco Asensio were erratic up front and could not find a way to break the deadlock as Atletico held fast with a five-man defence.
Diego Simeone, who equalled Luis Aragones as the manager with the most games in the history of Atletico in all competitions (612), had to make an early substitution when left fullback Reinildo Mandava was carried off on a stretcher with a left knee injury.
Even after substitute Angel Correa got a straight red card in the 64th minute for an elbow to the chest of defender Antonio Ruediger, Real still struggled to create chances.
Atletico ended up opening the scoring when defender Jose Maria Gimenez scored with a header from an Antoine Griezmann free kick in the 78th minute.
Real tried to make a late run and 18-year-old forward Alvaro Rodriguez levelled the match seven minutes later with a clever header in traffic from a Luka Modric corner.
(With inputs from Reuters)