This is normal behavior if you have never synced with this particular computer before. You would have recieved a popup explaining this. Has the iPhone ever been synced to iTunes on any computer. If so you need to move your iTunes folder from the old computer and replace the iTunes folder on the new computer.
If it has never been synced then you are out of luck.
How did the songs get on the iPhone? Were they iTunes purchases?
If so you can redownload them here:
From the Phone: Make sure you are signed in (settings > iTunes & App Stores) then open the iTunes Store app > More > Purchased > Music
On the computer: Make sure you are signed in and the computer is authorized then Open iTunes > Go to iTunes Store > Purchased (In the quick links section on the right) > Music
If they weren't iTunes purchases yopu need to retrieve the songs from your backup or where ever you keep them and add them to iTunes.
Then sync your phone.