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Gasperini's men have become renowned as one of Italy and Europe's most entertaining teams: they scored 98 times in Serie A this season and have averaged two goals for and two against per Champions League match.
The Bergamo region was hit particularly hard by the coronavirus pandemic, and Gasperini thinks Atalanta owe it to themselves and their supporters at home to stick to their principles in the quarter-final.
"We know very well the anticipation around this match, given the passion and love around Bergamo for Atalanta," he said.
"This year, there is even more motivation given all that has happened. It's a football match but we have to represent our region in the best way possible.
"We arrive in the best mental condition. We've got some very important results after the lockdown.
"We are proof that even a team without a European heritage can do well and achieve important goals through playing, enthusiasm and other things.
"We have a responsibility to ourselves not to disappoint. We want to continue to show that Atalanta can sit at the table of the biggest clubs."
The threat of Covid-19 means the remaining Champions League matches are being held as one-off ties behind closed doors in the neutral city of Lisbon.
Gasperini admits he would prefer to have a two-legged tie, saying Atalanta "historically have done well in the second match".
"We are facing a team we've never faced before and have no direct parameters in terms of meeting their players," he said.
Kylian Mbappe is an injury doubtand Angel Di Maria is suspended, but Gasperini expects his players to have their hands full when it comes to stopping Neymar.
"He is undoubtedly one of the strongest in the world. It's a problem for anyone to face him," he said.