Just another way to do it:

use strict;
use warnings;
use URI;

my $uri  = URI->new( $ENV{REQUEST_URI} );
my $page = ($uri->path_segments)[-2];
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The problem with this code is that the return value of URI::path_segments() changes if the URI contains a trailing slash or not. You could improve the robustness at the expense of added complexity by using map to squash the return of URI::path_segments() however:

my $page = (map $_ ? $_ : (), $uri->path_segments)[-1];
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Kinda defeats the purpose of using methods from a module however. ;)