Fede Dimarco struck the winner on Sunday.
Inzaghi later said: "I'm happy with the win.
“We played an excellent match. But based on how we played, we didn't need to suffer in those last ten minutes down a man.
“We were a bit imprecise in front of goal.
“And their goalkeeper made some excellent saves. But I'm satisfied with the guys' performance. The approach they took in both halves.
“We were up against an Empoli team who were very motivation after changing coaches."