In my opinion, the best way to increase your programming skills is by solving your own problems. Think of something you do often, and that you think could be automated. Scratch your own itches.
The exercices in the books have already given you a good overview of common algorithms, Perl features and other programming languages' strengths. Trying to solve a problem that bothers _you_ is the best way to become intimately acquainted with the features you need. It'll also teach you how to look for the things you need to solve your problems.
Search perldoc, PerlMonks and CPAN. Read code out there that almost does what you want, then modify it to suit your own ends.