Sevilla were crowned 2014 Europa League champions when Benfica strikers Oscar Cardozo and Rodrigo both had their penalty attempts saved, before Kevin Gameiro converted the decisive spot-kick for the Spanish club.
But it was Benfica that made most of the running during the initial 90 minutes and extra half-hour before the shootout, taking 14 shots to Sevilla's seven, although Jesus' men were unable to score.
"When you lose it is always difficult," the 59-year-old Portuguese coach told Benfica's website.
"During the 120 minutes we felt that we were team that did the most to win and we had more opportunities."
Benfica have already won Portugal's Primeira Liga and Taca da Liga this season and could complete a domestic treble if they overcome Rio Ave in the Taca de Portugal final on Sunday.
Jesus reminded both his players and Benfica supporters to immediately switch their focus to the cup final, as they also lost the Taca de Portugal last season.
"I congratulate the Benfica players and supporters, who were worthy of us once again to this end," he said.
"Now we have to look forward because we have another final on Sunday. "
The loss continued the fabled curse of Bela Guttman, as Benfica lost their seventh European final since winning consecutive European Cups in the early 1960s.
Guttman led Benfica to victory in the 1961 and 1962 European Cup finals but, when denied a pay rise, the Hungarian coach left the Lisbon-based club and reportedly declared they would never win another European title.
Wednesday's defeat was the second year in a row that Benfica fell at the final Europa League hurdle, having lost 2-1 to Chelsea last year.
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