For Gasperini to turn a good season into a great one, the Italians must beat the German champions in Dublin on Wednesday.
"They dominated the Bundesliga and are like a tank, but we are not afraid of them and will go there to play with courage and in good shape," he told Sky Sport Italia on Saturday.
Xabi Alonso's Leverkusen became on Saturday the first team to complete a Bundesliga season without losing a match, stretching their European record unbeaten run across all competitions to 51 games.
The club hailed the achievement by giving themselves a new nickname on their social media channel - "Bayer 04 Neverlusen".
"I think about that, I also think every run has to end sometime," Gasperini added. "Atalanta can trouble Bayer Leverkusen too."
The Bergamo club qualified for the Champions League with a 2-0 victory at Lecce on Saturday, providing some consolation after losing the Italian Cup final to Juventus last week.
"As far as we are concerned, Champions League qualification is an extraordinary result and these lads are going beyond all expectations," Gasperini said.
"I am truly happy with this and we need to dedicate it to everyone in Bergamo."
Gasperini has been linked with a move to Napoli and he did not rule out leaving Atalanta after eight years in charge.
"We are playing Wednesday, then after that we'll see," he said.
"What the difference means to me is the challenge and whether it is credible in the choices and evaluations, that is the most important thing."