New signings Mateo Retegui and Marco Brescianini both struck doubles on Monday night.
"We pulled this excellent performance out, it was great in every respect,” Gasperini told Sky Italia.
“This team was in a seemingly difficult situation, but these lads can push past everything, they just get on the pitch and play well. They were eager to play the first game of the Serie A season and did it really well.
“I have to congratulate them. Retegui has been here a little longer, but Brescianini only arrived a couple of days ago. They are players I know very well as Serie A opponents and it is to their credit that they settled in so quickly.
“Clearly, there is also a team putting them in a position to do well and get the best out of their characteristics, but they did a brilliant job.”
Atalanta were missing six first teamers through injury and also Teun Koopmeiners and Ademola Lookman, who are trying to force through moves away.
Gasperini also stated: “In all honesty, nobody expected to find ourselves in this situation. At this moment, I am having to take it one day at a time. I had a few thoughts after the Super Cup, but then we ran into all these difficulties, including Scamacca’s injury.
“I don’t know what will happen over the remaining 10 days of the transfer window. My job is to assemble the best squad possible, to see with the club what could be useful to add.
“Clearly, we’ll not have a defined squad until August 31.”