A fine early strike from Luis Suarez after terrific work from Marcos Llorente put Atletico in the ascendancy on home soil, but they could not hold on to a narrow lead and Karim Benzema fired an 88th-minute equalizer to keep the visitors in with a sniff of a successful LaLiga defense.
Seconds before Benzema tucked the ball past Jan Oblak, Suarez attempted to play in Saul Niguez for a chance to double Atletico's lead, but the striker's pass was poorly executed.
It was a reminder of how quickly games can change, and it remains to be seen whether Benzema's goal proves a turning point in the season.
Atletico had been heading five points clear of second-placed Barcelona and eight ahead of Madrid, with a game in hand on both, but now those gaps are three and five points.
A return of nine points from Atletico's last six games has allowed the big two in Spain to close the gap on Simeone's pretenders to the throne.
The Atletico boss was asked whether a big opportunity had been missed and said: "I don't want to be extreme in what I say. I took away many important things.
"People thought we were going to win by 20 points, [but] we are playing against very powerful teams, Madrid, Barcelona, Sevilla.
"It is going to be a difficult road for all of us and we want to improve on what we did last season."
Atletico were third last term, finishing well behind champions Madrid and Barcelona, and the signing of Suarez from the Blaugrana has proved a masterstroke.
The Uruguayan's 17th LaLiga goal of the season was a delicious finish, and one of the positives Simeone might have pointed to.
Yet after losing to Madrid away from home earlier this season, Atletico appear to have a major problem with their city rivals.
It is now 10 successive LaLiga derbies without a win against Madrid for Simeone's side, who have drawn six of those games and been beaten in the other four.
At least this time they were the better side for a large part of the game, but Simeone must wait to overtake Luis Aragones as the coach with the most wins as Atletico boss. He remains on 308 – the same number former Spain boss Aragones achieved across four spells in charge.
"I am happy with the team's work until the 80th minute and it's a shame that we could not win a game that we wanted to win," Simeone said.
"From the negative side there is the draw in the last minutes on one of their two chances in the game and the positive side is the good game we played.
"We were well controlled, we played a good first half. In the second we started with the same tune, with chances to be able to close it out and we could not be forceful.
"We were playing a team with great footballers who always have this in the last minutes. We had more chances to win it than they did."