Here are three tricks you could try, all of them analyzing the file where iTunes stores its "pointer" information. They won't help you get the music, just the metadata.
1. Look in your Music folder. Inside it, open the iTunes folder. Inside it, control-click on file iTunes Music Library.xml, select Open With, and choose application TextEdit. If things go right, you will be looking at a big file full of structured keys and values representing your entire iTunes library. Looking through all that data might be hard, but in it you may find the artist names and track names of the songs you deleted.
Be sure to Quit from TextEdit without saving!
2. Since you didn't previously have Keep iTunes Music folder organized checked, I'm not sure what information this will get you, but if you make sure to cut and paste this string exactly as I have it below, it won't hurt to try. Here's what to do: Open the Terminal application in the Utilities folder of the Applications folder. It should give you a command prompt of some kind. Cut and paste the following big long string as a single line (even though it looks like multiple lines here in the forum display), paste it into the Terminal window, and then press return.
grep '>Location<' ~/Music/iTunes/iTunes\ Music\ Library.xml | cut -d: -f2 | cut -d\< -f1 | sed 's/%20/ /g' > ~/Music/iTunes/Lost\ Music.txt
Quit from Terminal.
Then, back in the Finder, double-click file Lost Music.txt in the iTunes folder of your Music folder. It should have a list of paths to your former music, which may include the artist and track names.
3. The same as #2, but with a different command to find song names and artist names, rather than the paths to the music files. Again, you paste this into a Terminal window and it is one long line. The results will be in file Lost Music2.txt
egrep 'Name|Artist' ~/Music/iTunes/iTunes\ Music\ Library.xml | cut -d\> -f4 | cut -d\< -f1 | sed 's/%20/ /' > ~/Music/iTunes/Lost\ Music2.txt