The two teams will meet next week in Warsaw.
Gasperini said, "That will be an extraordinary occasion for Atalanta, for Bergamo, for the history of the place. We are playing against the most decorated club in the world, against the team that has won the most in the world. To play a final like this, for this trophy against such an important club, would have been unthinkable until fairly recently.
"There's a huge sense of pride. Also, a feeling of wanting to be there, of wanting to go there and put in a great performance and hold our own against a club who are historically the stronger team. It's a really inspiring moment for the whole of Bergamo, all the fans. There's no doubt it's a high point, perhaps the pinnacle in the history of Atalanta."
On Carlo Ancelotti, who he worked with at Juventus, Gasperini said: "Carlo is clearly an institution the world over. He is without question the coach who has won the most. He's done that with many different clubs, and he is doing amazing things at Real Madrid. He did it before with them and he's doing it again.
"Clearly for us, at least for me anyway, it will be very special to be playing against him in this final, considering 30 years ago I was coaching the youth team at Juventus and he was coaching the first team. That was many years ago, but it will be wonderful to meet again in this final."
On winning the Europa League, Gasperini also said: "It was a long journey in the Europa League. From the first game in Lisbon onwards, we showed our qualities and played to the best of our ability. It was a really high-level competition and winning it that way was a huge achievement for us.
"We were the underdogs against Liverpool, maybe against Sporting CP too at the start. Everyone thought they would win – and in the end we faced them four times (group stage then round of 16). I should say that being the underdogs worked in our favour to a certain extent, it brought out the best in us.
"I don't know if we were one of the best teams but we were very good. We were definitely the best in the competition, partly because of the results we got: 3-0 against Marseille, 3-0 against Liverpool, 3-0 against Bayer Leverkusen. There were other games too, like our ties against Sporting where we beat them twice and drew twice.
"We did ourselves justice throughout the Europa League and the most satisfying thing is that competitions like this are really uncertain – they can pivot on a single incident – but it is widely recognised that we deserved to win the trophy."