Jose Gimenez struck the winner on 90 minutes for Atletico.
Simeone later said: "The boys played a great game. It was a shame to lose those two points. They took advantage of a counterattack and then we controlled their attacks very well. We attacked in different ways, with Correa, Julián, Griezmann... In the first half we had three or four chances that we couldn't score and in the second we controlled it better.
"We spent a period between the 70th and 80th minutes where it seemed like the game could get away from us and Giménez's goal came. Very good work from the team, the outside players entered very well. If we manage to get the outside players to enter well, we get what we are going to look for.
"I am totally satisfied, the match was very good. I would have said the same thing about a draw. We played the match in different ways and with different players. The players interpreted it well and we won a necessary match."
He also said: "In the second half we started with a 4-4-2 with Correa on the right and Riquelme on the left. We needed more legs in the middle and a reference with the possibilities that Sorloth gives us and with Lino we wanted to change Riquelme's dynamic. The three changes were interesting, they generated better content from the game.
"Then we saw Ángel more tired, who played a great game, and Nahuel came on who was very good with Marco. We put a slightly stronger midfield with Llorente, Gallagher, Lino, Koke and Sorloth to contain the midfield. That's how the goal came at the end, but it could have come much earlier."