You can skip the expense of holding the complete uncompressed zip file in memory and stream directly from the zip files as shown below.

use IO::Uncompress::Unzip qw(unzip $UnzipError);

my $logDirectory = '/logs';
foreach my $zipFile (glob("$logDirectory/*.zip")) {
        my $output;
        print "Processing $zipFile\n";

        local $/ = "\r\n";
        my $unzip = new IO::Uncompress::Unzip $zipFile
            or die "Cannot open $zipFile: $UnzipError\n";

        while (<$unzip>) {
                #do something
        }
        close $unzip or die $!;
}
[download]

Doing it like this means that the complete uncompressed zip file doesn't not need to be stored in memory.

Also note I set $/ to "\r\n" as you say that the data uses this to delimit each log entry.