After taking the lead through Andrea Poli's eighth-minute strike, Milan failed to assume full control of the game and were punished by a clincial Sassuolo side.
Nicola Sansone levelled matters in the 28th minute, with the match then settled in the 68th minute courtesy of Simone Zaza's stunning first-time volley from a Domenico Berardi corner.
And Inzaghi has called for his side to respond after an error-strewn display.
"I think the first 20 minutes deceived us, made us think that it was all easy," Inzaghi said. "But in Serie A, nothing is simple, especially against such an organised side.
"We became imprecise, a bit sluggish and things then went wrong. I am disappointed as we were doing very well and this is a step back. This match will serve us as a lesson. This side needs to grow.
"We deserved to lose and now we must be good in picking ourselves up right away. We made more mistakes than usual. The match after the winter break always has hidden dangers, we prepared well, but matters on the pitch say otherwise.
"In the second half we enjoyed more than 60 per cent of the possession and perhaps we should have created more chances. We conceded from a corner and this cannot happen as they took just one corner in the entire match.
"We have to be more clinical in these matches. When you lose you have to take responsibility, we must look at what went wrong.
"The first 20 minutes were up to the Milan standard, but it's not enough. We must roll our sleeves up...and prepare for a hard match against Torino."
Meanwhile, Sassuolo boss Eusebio Di Francesco hailed his players for what he described as a "daring" showing
"I expected Milan to have a strong start, but then we had a great first half overall and could've gone in front before the break too," Di Francesco told Sky Sport Italia.
"In the second period we did well to contain Milan and score on a corner that we had practiced in training.
"I think it really helps a team to be daring and show no fear. If players feel too much pressure, they cannot express themselves to their full potential.
"I like this mentality, as we press at the right times and caused Milan a lot of problems. The win was thoroughly deserved."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
