Atalanta are in second place, two points behind Napoli after 10 games, and extended their unbeaten run from the start of the season to a club record 10 matches with a 2-1 home win over Sassuolo on Saturday.
"The world of football pushes in another direction, maybe towards the teams who have a bigger following. It looks like the first requirement to compete - not soccer, but the number of fans," Gasperini told RadioRai.
"We, with our resources, cannot say that we will fight for the Scudetto."
Gasperini took over in 2016 and led Atalanta to their first ever Champions League qualification in 2019 followed by two more seasons in Europe's elite club competition.
The finished eighth in Serie A last season and failed to get into Europe for the first time since Gasperini became coach.
"Maybe we will aim for the Italian Cup, which is already a difficult target: otherwise I can say that having reached the Champions League for three times in a row is like switching on the spotlight," he added.
Atalanta face either fellow Serie A side Spezia or Serie B club Brescia, who meet on Wednesday, in the Italian Cup last 16.