First half goals from Alessandro Florenzi, Francesco Totti and Maicon gave Roma a huge platform before Mehdi Benatia headed a fourth in the second half to seal the Grifone’s fate.
“A defeat like that can happen,” admitted Gasperini to Rai Sport.
“Roma, Juventus and Napoli are on a different level.”
Gasperini was also critical of Matuzalem after the player was sent off off for gesturing to the crowd as he was substituted.
“The player made a mistake, he made a gesture towards the fans which is why the referee showed him a second yellow card,” the tactician added.
“It is a pity as he will not be available to us for the next game which is crucial to us.”
Genoa are on a poor run of form, recording just one win in their last seven league games and currently sit tenth in Serie A with 23 points.