But Simeone said he was happy with how his team reacted to conceding an early goal, adding that he felt confident they could turn the tie around in the second leg at the Metropolitano stadium next week, as they did against Inter Milan at the same stage last year.
"We should have taken better advantage when we had control of the game," Simeone said.
"It's difficult to take risks so that with any counter-attack you end up losing the game. We controlled that situation very well, but we were missing (something) in the final metres."
The Argentine said he was confident that the atmosphere at their home ground would give Atletico "a stimulus" and that while his team go into the second leg behind, it could have been much worse had Real taken a late chance on Tuesday.
Real's Kylian Mbappe failed to find Vinicius Jr with a pass in the final moments of the match that could have led to another goal.
"Maybe the hope of that no goal opens the door for what's to come," he said.