Welcome to Android Central! Did you save those contacts to your Google account, or to the local Phone account? If they were saved to your Google account, then they should have automatically synced with your Google Contacts in the cloud--go to that website and see if they're there. If they were saved to the local Phone account, then it's going to be very difficult to retrieve them, because those don't sync anywhere automatically, and they're saved in an SQLite database file on a protected system directory. So you wouldn't be able to access it unless the phone is rooted.
In the future, I strongly recommend you save all of your contacts to your Google account, or some other account that automatically backs up somewhere.