Goals from Luis Suarez and Yannick Carrasco sealed all three points for the visitors, with Torreira completing the full 90 minutes in central midfield alongside Koke.
Simeone was pleased with the Uruguayan's performance and believes that his physical qualities can contribute positively towards Atletico's season.
"He is a very hard-working boy, we are going to need him," he said following the final whistle.
"He competes very well, he will give us a lot of strength there in the middle of the court, when he obviously picks up the pace of the game.
"His speed characteristics, going out quickly in the circulation of the ball in the middle will generate more speed in that part of the middle of the pitch and well, hopefully he will find the best form."
Torreira was struck by cramp during the latter stages of the match but showed great determination to carry on, which generated additional praise from his new boss.
"We knew that such annoyances could happen because it had been a long time since he played in this situation," Simeone continued.
"But from his first day here he showed what his characteristics were – a guy who is going to give absolutely everything."
The 24-year-old made 39 appearances for Arsenal in all competitions last season, scoring twice and assisting once.