This happens quit often via Eurail reservation service. You should reach Trenitalia Customer Service to get this modified for you. With an 2nd class Eurail Pass you are not allowed to use 1st class without paying the difference between 1st and 2nd. 

Also you can change it at the ticket office in the station or the last minute “Freccie” kiosk in bigger stations. They will change it without fees for you (but only if free seats are left in 2nd class), or in case this is not possible, ask before before boarding the train directly Trenitalia train staff. They can find a solution for you. 

Thank you so much for the fast response! I’ll contact Trenitalia directly!

Update: Trenitalia customer service stated that they cannot help me change the ticket, that I would need to contact https://trenitalia.interrail.eu/en/global-pass or the ticket offices in Italy which is ridiculous, especially if you need to arrive around a certain time and if it so happens there are no 2nd class seats available. Not to mention I am not in Italy yet… this is something that needs to be fixed! This is too much of a headache for me to have to go out of my way to fix a booking system error, when Eurail has not responded to my emails for over a week, and Trenitalia cannot help me via online. 

Thank you so much for the response Angelo! I will have to wait until Eurail contacts me, or once I reach Italy. 

Next time, book via ÖBB using these steps. Or from an Italian ticket office. Both are cheaper than via Eurail (no booking fees).

Thank you @rvdborgt for the information! I only made 1 reservation via Eurail so far because we need to be at a destination before a certain time. I’ll definitely book the rest of our reservations at the ticket office!

thanks!