Gasperini left Atalanta and was named new Roma coach last month.
"Roma has made a great move with Gasperini," Panucci told Napolimagazine.com.
"It is clear that he will find himself in a different place from Bergamo. His way of working and playing needs time, but in Rome this, at times, is a rare luxury. However, the owners and fans have understood that Gasperini needs to work without too much pressure to bring important results."
Panucci then also commented on the changes that have taken place at the management level.
"They were good at doing a bit of self-criticism and realizing that they had made mistakes in the past. (Claudio) Ranieri has changed roles and a new sporting director has arrived, it seems to me that the American ownership has sent a clear and strong signal of change at all levels."