The Champions League semifinalists were stunned 3-2 on the night, with Thiago Almada shown red for Atletico on the half-hour mark.
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Asked about the dismissal, Simeone insisted: "We started the game well, playing where we wanted. Then the player was sent off, but the lads were competing well.
"We gave it our all to get a point, and I take full responsibility for everything that happened to the team."
It's now four consecutive defeats for Atletico.
Simeone also said: "I trust them completely. I know they'll get through the situations we're going through, but I trust them."
