Raul Garcia's 14th-minute strike was enough to hand Atletico the narrow victory, keeping them one point ahead of Barcelona and three points clear of Real Madrid, both of whom won later in the day.
The leaders were forced to hang on in the closing stages of the match, and Simeone was effusive in his praise of the team's character towards the end.
"We've been making a huge effort, incredibly so, I can't find the words to keep congratulating the players' effort. It was a complicated match and we achieved an important victory," Simeone told the club's official website.
"At the end we were tired, which is normal. The strength and energy we had in previous occasions were not there, but the team was level-headed, and that made up for the lack of energy."
In addition to their title aspirations, Atletico are also 90 minutes away from the Champions League semi-finals having drawn 1-1 with Barcelona in the first leg of their quarter-final clash.