Simeone believes the midweek exertions took a toll on his players, and was grateful to goalkeeper Jan Oblak for making sure they at least returned home with a point.
"We weren't as convincing as we should have been in the first 15 or 20 minutes," he told the media.
"We had opportunities to score, but didn't. After that, it was normal that our players were tired, since we played on Wednesday night.
"We attacked without clarity and they had some good chances on the counter, but Jan [Oblak] was secure in the back."
0 - Antoine Griezmann has failed to register a single shot in a game for the first time this season (all competitions). Vigilance. pic.twitter.com/i3r5kpdxpP— OptaJose (@OptaJose) September 30, 2017
The Atletico head coach made changes in an attempt to freshen things up, including picking three centre-backs in his starting XI and pushing Saul out to the left of midfield.
However, defender Jose Gimenez - who came close to opening the scoring inside two minutes - acknowledged the visitors struggled to break down a Leganes defence that has conceded just three league goals this season.
"We knew it was going to be a difficult match. They played a smart match and we could not score the goal," he told the media.
"It would have been important to win today, but now we have to continue working because we have room for improvement."