The Module::ScanDeps module will recursively find all modules used by your scripts. It will also find all core modules, so you need to sort out what you do and don't need.

use strict;
use warnings;
use Module::ScanDeps;

# insert your script(s) name(s) here
my @scripts = qw/ myscript.pl /;


my $hash_ref = scan_deps(
     files => \@scripts,
    recurse => 1,
);

print $$hash_ref{$_}->{'key'}."\n" for sort keys %$hash_ref;
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Ideally though, you should just use CPAN to install the necessary modules.