Former Milan defender Luca Antonelli scored the only goal of the game with a first-half header at the Stade Luigi Ferraris as the home side extended their unbeaten run in Serie A to nine matches .
The Genoa skipper's winner moved his side third as Milan were left to rue a lack of guile on a frustrating outing for Inzaghi's men.
However, former Milan striker Inzaghi maintains he can get the club back into the upper reaches of Serie A again given time, adding that his side may benefit from the defeat in the long run.
"I knew there would be highs and lows in the reconstruction process," Inzaghi told Sky Sport Italia.
"Nobody can say we don't play and fight for every ball but today we were probably lacking that clinical edge in front of goal.
"That is football and at times this side needs this type of defeat to learn. Despite the defeat, I thought it was a good performance.
"After the break we tried everything and got a bit too stretched out, but didn’t get the equaliser. Unfortunately at that moment when we need to make that step up, we are still lacking something.
"Next we have more important tests against Napoli and Roma."
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