Do you believe this business has committed fraud? For example, did you select a vase in the shop with a promise that that specific vase would be sent to you and then get sent a different object? If that is the case, you can report at https://www.econsumer.gov/#crnt (this is the official suggestion of the Federal Trade Commission). If you scroll all the way down to the bottom, you see some links for Other Steps You Can Take. You may want to check those suggestions before filing an official complaint.
(The difficulty for you, in that case, would be proving that the object you saw in the shop is not the object you were sent--you don't happen to have pictures of the object in the shop, do you?)
I've been very lucky so far in my dealings with businesses in Italy, so I have no personal experience in this matter. However, my understanding is that there is little the Italian authorities may be able to do now that you are no longer in the country. You can file a complaint here: http://www.agcm.it/en/component/content/article/11...
If the business did not give you an official fiscal receipt, you will definitely want to mention that in your complaint, as that is a strong indication they are committing tax fraud. The Italian government takes that very seriously and might even forward the issue to the Guardia di Finanza.
Unfortunately, if the business was just shady, your options are much more limited. For example, if they said they would send you a vase similar to the vase you saw in the store, you're surely out of luck from a legal perspective. You could consider filing a payment dispute (I am assuming you did not pay in cash). You could try leaving reviews (make sure they are very calm-sounding or else no one will take your complaints seriously) along with pictures on websites like Yelp or Trip Advisor, and that might spur the company to reach out to you.