I'm a dual US/Italian citizen and before my most recent trip to the US I had always used my US passport to enter the US when going there. When exiting, I would use my US passport and then also show my Italian ID card to Dutch authorities when arriving there to prove my EU citizenship (I live there).
This year I decided to also get an Italian passport as proof of my EU citizenship since the ID card was starting to wear and Dutch customs officials were pointing this out each time. Now not being familiar with how to travel with two passports, when I checked-in at the self-service kiosks at the airport in the US on my date of departure I used my Italian passport instead of my US one (which made sense to me at the time). I did use my US one to get in the country, but I've read that one must use their US passport to both enter and leave the country.
Are there consequences I am going to face for this? Is there any way to correct my departure information from the US with the authorities?