Recovering the contacts, SMS and call log from SD card
Your assumption that Contacts, SMS and Call Logs are automatically saved to the SD Card was incorrect. They are indeed stored on the internal memory of the device. /data/data/com.android.providers.contacts/ is the most likely storage location. That can change though, depending on Android OS version, manufacturer/carrier modifications, or even 3rd-party apps that you use in place of built-in Contacts/Phone/Messaging apps.

Unless you synced your contacts to your Google account, backed up SMS and call logs, they are now lost after a factory reset.