The 3-0 win against Bayer Leverkusen marks a second Europa League title for Zappacosta, who also lifted the trophy as a Chelsea player.
He later told Sky Italia: "It's the second time I've won it, I'm proud of the progress made with the boys. We beat strong teams and tonight we gave an absurd demonstration of strength. We're very happy.
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"It has always been there, we have always faced anyone knowing we could win. An incredible result. Matches like the one against Liverpool give strength, but in general we have had an extraordinary season
"The coach prepares us all in the same way and certain challenges come by themselves... We pushed, always shortened, we deserved the victory."
Asked if a success with Atalanta was better than with Chelsea, Zappacosta added: "It has a greater weight and a different flavour. I am convinced that excitement will await us in Bergamo."