The La Liga side claimed a 4-2 penalty shootout win over Benfica in the final, which finished 0-0 after 120 minutes at the Juventus Stadium.
Benfica had enjoyed the better of the opportunities throughout the encounter but two saves in the shootout from Sevilla goalkeeper Beto were the difference.
Emery hailed his side for being prepared to work and fight late in the contest.
"Benfica have been deserving finalists, as we have," he said.
"There were times when the the match was very even. We were expecting some chances, like the one for (Carlos) Bacca, but we had to be prepared for anything. In the end they made the last push.
"You could see the tiredness and discomfort of the players but this team has learned how to suffer, has learned to stay big and was prepared for this."
Beto kept out Benfica's second and third spot-kicks, albeit coming a fair distance off his line to deny Oscar Cardozo and Rodrigo.
Emery praised the goalkeeper and goalkeeping coach Javier Garcia Garcia.
"Javi has done a great job with the goalkeepers and with Beto has been crucial," Emery said.
"It's the work of a lot of people."
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