Luis Alberto grabbed a second-half winner.
“It's an important victory and the lads put in a strong performance," Inzaghi told Sky Sport Italia.
“Frosinone were very focused, but Thomas Strakosha never had to make a save. We can say that our season starts now.
“They say fortune favours the brave and we've got to go looking for our luck. The goal seemed almost cursed again tonight, but we found a way through.