The 48-year-old was charged with improper conduct by UEFA after celebrating Jose Gimenez's opening goal in the 2-0 win by grabbing his crotch.
Simeone attracted criticism for the gesture but he apologised after the match, explaining it was directed at Atletico fans to show them that the team "have cojones".
He told reporters: "It means we have balls, a lot of balls.
"To start [Diego] Costa and Koke after they hadn't played for a month takes balls."
"It wasn't aimed at the other team, I was turning towards our own supporters.
"It's not a nice gesture, I'll admit, but I felt the need to do it. It was such a tough game, we fought so hard and Diego Costa worked really hard when he wasn't 100 per cent fit. I had to show what I was feeling.
"I can only apologise if anyone was offended, but I did it from the heart.
Simeone has now been sanctioned by UEFA's Control, Ethics and Disciplinary Body, but he will be free to be in the dugout for the second leg at the Allianz Stadium on Tuesday.
The Argentine tactician has said of a return date with Juve: “The tie is not over yet, there is still a game to play.
"For sure we will have to suffer against a great opponent, with great players.”
On top of Simeone's sanctions, Atletico have been fined €38,000 for breaching regulations relating to blocking stairways and throwing objects.
Juve have been ordered to pay €30,000, while head coach Massimiliano Allegri has been warned, because of the game's late kick-off.