With Atletico trailing 1-0 in the first leg of their last 32 clash at the Vicente Calderon, goalkeeper Sergio Asenjo surprisingly ventured forward after the home side won a corner four minutes into stoppage time at the end of the match.
Rubin then cleared the corner before breaking away and, with Asenjo still struggling to get back, Pablo Orbaiz was able to slot into an empty net and give the 10-man Russian side a vital second away goal.
Simone accepted responsibility for Asenjo's venture forward after the match, saying: "The decision was mine. I thought the game was finishing and 1-1 would have given us a much better chance. And football is a game of risk.
"This time it turned out bad and means we now have to score twice in the return leg."
Gokdeniz Karadeniz's sixth-minute strike put Rubin ahead but Atletico received a boost on the stroke of half-time when the visitors lost Roman Sharonov to a second yellow card.
However, Atletico could not take advantage and suffered a late sucker-punch with Orbaiz's breakaway goal.
Simeone said: "We had a lot of chances but we lacked speed to create more situations. They defended well, but we should have got a draw at least."
The defeat ended Atletico's 21-match winning streak at the Vicente Calderon, but more important was the damage it did to the defence of their Europa League title.
Asked what what chance the Rojiblancos had of turning the tie round in Russia, Simeone told reporters: "very little."