Atletico and Chelsea could not be separated in the opening leg of their semi-final tie at the Vicente Calderon, with Jose Mourinho's men frustrating their Spanish opponents throughout.
The La Liga leaders dictated play for most of the contest but despite boasting star striker Diego Costa, they lacked cutting edge up front with the team failing to create any real clear-cut opportunities as Chelsea left Madrid with a valuable clean sheet.
And the advantage is now with Chelsea heading to Stamford Bridge for the return leg in London next week, according to Simeone.
"It was a difficult game, tough and typical of semi-finals where neither side could take the advantage," said the Argentine, whose side were held scoreless at home for the first time since February.
"We offered different things with our play, but we just couldn't find the goal we needed to win the game.
"They have the advantage with this draw but whoever gets the victory will go to the final."
Atletico were thwarted by a resilient Chelsea outfit, who were set out to sit deep and break up the play.
Former Atletico striker Fernando Torres was deployed as a lone striker as Mourinho opted for a five-man midfield and it worked effectively.
Mourinho's defensive tactics were criticised by pundits and sections of the media but Simeone refused to condemn the controversial Portuguese tactician.
"Each manager chooses what best suits the players available to him," he said.
"In the end, it's brought him a positive result."
On top of their frustrating evening in the Spanish capital, Simeone must also contend with a fatiguing squad that has played a staggering 57 games in all competitions.
"It's true, we'll have to make a huge mental effort, but it's a nice concern to have, because we're fighting for wonderful things," he said.
