Through to the last four of Europe's elite club competition for the first time in 40 years, La Liga leaders Atletico dominated the ultra-defensive Premier League club at the Vicente Calderon but failed to find a goal and face a stiff task in the return in London next Wednesday.
"It was a difficult game, tough, typical of a semi-final, in which neither side was able to grab the advantage," Simeone told a news conference.
"We each approached the game in different ways but we couldn't find the goal that would have won the match," added the Argentine, who has transformed Atletico into a genuine force in Spain and Europe since taking over at the end of 2011.
"Each person chooses the best strategy according to the players he has. In the end, he (Mourinho) got a good result.
"At their stadium, with their fans and their atmosphere, they will feel more comfortable but we will fight with humility."
Mourinho, back in Spain for the first time after three years in charge of Atletico's city rivals Real, was unapologetic about his team's cautious tactics.
The Portuguese is in the Champions League semi-finals for the fifth year in a row after appearances with Inter Milan in 2010, when they won the title, and Real in 2011, 2012 and 2013.
"It was a match for men, hard-fought, tactical, balanced," he told Spanish television.
"Atletico dominated more but despite the problems we had we came away with this result in what was the match of their lives.
"Now there is another game and it is at Stamford Bridge. It is not an incredible result but I knew it was not going to be easy to avoid defeat and we managed it."
Chelsea will be without goalkeeper Petr Cech and captain John Terry in London, who were injured on Tuesday, as well as suspended midfielders Frank Lampard and John Obi Mikel.
However, fullback Branislav Ivanovic, who missed Tuesday's match through suspension, should be available and Mourinho said he had every confidence in stand-in keeper Mark Schwarzer.
Asked if he planned to use more attacking tactics in the return, he added: "It's a good question but I am not going to answer."