Players from both sides were struggling with cramp as extra time dragged on but the Spanish side triumphed on penalties to win the European trophy
The Spanish side was arguably the underdog heading into the final in Turin but fought until the end of extra time - through cramp and exhaustion - to reach spot kicks.
Sevilla scored all four of their penalties - as Benfica missed two of their first four - to secure its third win of the secondary European trophy in the club's history, and Emery praised the way his team battled beyond the pain barrier to triumph.
"Benfica are a great team," the coach told Cuatro. "At the end of extra time we were tired but we've learned how to cope through suffering with solidarity. This title is down to so many people."
Sevilla substitute Kevin Gameiro scored the winning penalty and admitted that it did not cross his mind how he would take the penalty, while stressing how crucial the victory is for the Spanish club.
"I didn't think when I was shooting the penalty," the French striker said. "I just kicked it hard. It's a very important day for us."
Between the sticks, meanwhile, Beto put in a great performance to keep Benfica from getting on the scoresheet and saved two penalties during the shootout to help his team conquer Jorge Jesus' men.
"It's the perfect final," the goalkeeper said. "It ended the best way. I'm so proud being part of this team and I'm so happy to win this trophy."