Ideally you would have kept the old computer running until you were happy that the new computer was running properly with all of your content.
Ideally you would have a full backup of your data to hand, ready for restoring to a new or repaired computer in the event of a problem. If you have such you can try restoring a working version of your library from that.
If you think your transfer process should have included the library database and not just the media did you try the suggestions in Empty/corrupt iTunes library after upgrade/crash?
I have a scripting solution for importing device playlists using iTunes for Windows, but I'm not aware of anything directly equivalent for Mac. There are however some general recovery tools such as those mentioned towards the end of Recover your iTunes library from your iPod or iOS device, some of which can pull back playlists too.