The Spanish side won a penalty shoot-out 4-2 after extra-time at the Juventus Stadium in Turin to clinch their third European title while consigning Benfica to their eighth straight defeat in a European final.
Carlos Bacca missed a late chance to win it for Sevilla in normal time while goalkeeper Beto was kept busy by the Portuguese champions, for whom Nicolas Gaitan and Lima came closest to scoring.
Oscar Cardozo and Rodrigo both missed from the spot in the shoot-out, but substitute Kevin Gameiro made no mistake when firing home the winning penalty.
And while Emery praised Benfica for putting up a good fight, he suggested his players had perhaps managed their energy levels better across the two hours.
He told AS: "Benfica deserved to be in the final and so did we. At times the game was totally even, put by the end they were doing most of the pushing.
"You could tell our players were suffering from fatigue and physical discomfort but this team has learned how to suffer.
"We have learned how to stay strong and so we were ready for that."
Emery reserved a special dedication for his coaching staff and made sure to single out goalkeeping coach Javi Garcia for competently preparing Portuguese stopper Beto for the big occasion.
"My family, my friends, the coaching staff deserve it for the hard work and dedication. And the team have stayed united during difficult periods," Emery added.
"The great work Javi has done with the goalkeepers and with Beto has been key.
"It's the result of a lot of people's hard work.
"We were expecting there to be some big decisive moment during the game, like the one with Bacca, but we were ready for any eventuality."