The reigning Spanish champions took on arch-rivals Real Madrid twice within the space of four days last week and Simeone feels fatigue was the main reason for his side's draw against Rayo.
"We came from playing against Real Madrid on Tuesday and Friday and the effort from these days could be felt in the second half," Simeone told reporters.
"Being so high up you couldn't see it as well, but I don't think that having me on the field would've improved anything."
Simeone lamented his side's failure to take their chances in the first half, but believes Rayo were the better team after the break.
"The first half, the team played very well. We had three clear chances of scoring, it was dynamic, but we couldn't score.
"The game lasts 90 minutes, though. In the second half, Rayo were better. We didn't play against a wall, we played against a team."