Raul Garcia's 14th-minute goal settled the contest, but the hosts had to withstand heavy pressure in the closing stages to see out the match.
"We've been making a huge effort, incredibly so, I can't find the words to keep congratulating the players' effort," Simeone said on the club's official website. "It was a complicated match and we achieved an important victory.
"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."
Atletico are now six games from the title, with a trip to Barcelona coming on the final day of the season, and the Argentinian admitted none of them would be straightforward for his side.