After initially falling behind to Karim Benzema's third-minute goal, Atletico forged a 2-1 lead at half-time thanks to strikes from Koke and Gabi.
They were denied several penalties by referee Carlos Delgado as Diego Costa looked to have been tripped by Sergio Ramos, Pepe and Alvaro Arbeloa, but each time Real escaped.
With time running out, Cristiano Ronaldo stole a late point for the visitors, denying Atletico a first La Liga derby double in 63 years.
The result left Atletico three points behind their neighbours in the race for the summit, but Simeone is still confident his side are serious title contenders.
"We went behind but reacted really well," he said. "We started to play between the lines, press them on the shoulder and create chances.
"In the second half we were good. We had opportunities but couldn't find the final pass to make it 3-1.
"The team put in great work. I'm proud of the squad.
"What counts is the final result. The team showed today it's alive (the title race). That might bother some, but we're still alive.
"Three points off the top with 12 games left is very good."
Simeone would not talk about the performance of referee Delgado, however, stubbornly making no comment on the official - who sent home coach German Burgos to the stands after a second-half confrontation - despite being pushed for an assessment.
"No, no, I'm sorry - I'm not saying anything about the referee," he added.
