Two second half penalties were enough to do for Betty Bavagnoli's side, who hit the post in the first half through Agnese Bonfantini but otherwise struggled to create clear-cut opportunities.
"We have to work on the errors, absolutely," Bavagnoli said after the game.
"The game could have gone a different way, instead we are talking about a defeat where there is not much more to say - we need to be humble and realise that in Serie A you need to play a certain way and you need to be clinical."
A mistake from Tecla Pettenuzzo then allowed Cecilia Prugno to open the scoring early in the second half from the penalty spot, a deficit the Giallorosse struggled to really bounce back from.
Then, with time running out, captain Elisa Bartoli was sent off after blocking a goalbound effort with her hand - the resulting converted penalty ending the contest.
With the international break now taking place, the team have a period to reflect on their start to the season.
"Now there is the international break, we will have a lot of time to analyse our performances and improve," said defender Angelica Soffia.
"We know that are lacking a bit of cutting edge in front of goal and that can make the difference."
See more photos from the game in the gallery below.
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