There are a few successful or least successful ways to recover your deleted contacts. The recommended one is to simply reconnect the Google account that you previously attached to your phone and then synchronize it. It's required to simply enable and disable WiFi to connect to a network and contact synchronization is done automatically.
Another possibility is with the help of an application, but it's not guaranteed that it will work properly, because those contacts had to be previously stored on the system partition and without root, any application that you want to try will be useless.
As a suggestion, you could try the applications on the following list. Download, install, connect the phone then attempt a possible recovery.
