phpMyAdmin and all things in XAMPP should work "out of the box" as this is essentially the intentions of the XAMPP developers.
If it helps I have searched around for a direct answer or fix for that error message but came up blank, so perhaps it may still point to an XAMPP install issue.
Did you set a password for the MySQL\phpMyAdmin user root
in the Security page?
Make sure Apache and MySQL are running.
Try this and see if it gets rid of the error message:
1. Click on the Security link in the left column menu on the Welcome Page.
2. Click on the http://localhost/security/xamppsecurity.php
link - there may be a delay while it loads.
3. Type in a password and repeat the password for the root user.
4. Make sure Cookie is selected (easier to repeatedly login using a cookie).
5. Click on Password Changing.
Now try phpMyAdmin again - you may have to restart Apache and MySQL - then enter root
for user and the password
you just set, if you get to the login screen that is.
If that does not work then you may have a corrupted install perhaps, so the best thing to do first would be to completely uninstall XAMPP and then delete the xampp folder...
...make sure all XAMPP components are stopped and if running as a service make sure that the services are uninstalled including the XAMPP Control Panel, often overlooked - then it is safe to delete the xampp folder.
Now install XAMPP again but may I suggest you download a fresh copy in case the download was corrupt for some reason - personally I prefer using a 7zip archive version and install it manually by extracting the archive to say C:\ or E:\ etc. as per the ApacheFriends web site - you may then have to run the setup_xampp.bat file to have your paths in XAMPP set correctly.