Real dominated the opening 45 minutes at the Vicente Calderon but could not find a way past inspired Atletico goalkeeper Jan Oblak.
And the repeat of last season's Champions League final finished 0-0, leaving both sides with everything to play for in next week's second leg at The Santiago Bernabeu.
Simeone was pleased with the way his men battled their way back into the match as Atleti's unbeaten streak against Real this season extended to seven matches.
"I want to talk about the game and assess the change in my team from the first half to the second," Simeone told AS.
"The tie is open after this result. The boys were able to react well. We talked [at half-time] about the football and what we were doing.
"The game is where it is. We're against a very strong opponent and I appreciate the change in the second half.
"We will go forward, calmly and to an important game. But it's all open."
Both Atletico's Mario Suarez and Real's Marcelo were booked in the second half, meaning they will miss the return clash.
"For both teams there have been heavy casualties," Simeone said.
Atletico forward Mario Mandzukic was in the wars, bleeding profusely after being elbowed by Sergio Ramos and he also tangled with Dani Carvajal on more than one occasion.
"The elbow was inadvertent," Simeone added.
"[Mandzukic is] brave. He made a great effort and we need him."
