Matija Nastasic struck just after halftime for Leganes' winner.
Simeone said afterwards: "We have played 15 wonderful games, a record in the history of the club, it was a very nice journey that benefited us in the League, Cup and Champions League. Today the team was able to get close to scoring in the final stretch of the game, they were also dangerous, the game was about trying to win it.
"After the goal they defended better and we lost height with Sorloth's absence, that's why we brought on Niño, but Leganés was very good defensively. We had the goal. I leave with congratulations to my players and the feeling that we made many important mistakes, but that the small details were against us this time.
"The team created enough to have a better score in the first half, then they worked very hard in the second. We had the penalty, the rival did very well and we had to lose. Now we have to face one of the best in Europe."
Simeone also reflected: "When you get used to winning, it's harder to lose because it's so nice. Obviously it hurts to lose, but it's part of the journey and you have to accept it.
"The year we won the league we lost to Levante and the other year to Almería. You can win and lose against anyone. Barcelona lost five and they are the best players, they probably shouldn't have lost any of the five."