Atalanta led twice through Duvan Zapata and Ruslan Malinovskiy, but Cristiano Ronaldo scored penalties to cancel out both goals, including a 90th-minute equaliser in Turin on Sunday (AEST).
While Gasperini was proud of his third-placed team, the Atalanta coach believes it deserved all three points.
"I'm definitely more proud. We played great in the first half and in the second half there was a comeback by Juve," he said.
"But with our play, we managed to take the lead and play a great game anyway. Of course, we are also upset because we deserved to win.
"But, in football, your performance is not always enough."
With six games left to play in Serie A, Atalanta is third in the table, nine points adrift of Juventus.