If hostname verification is requested by LWP::UserAgent's ssl_opts, and neither SSL_ca_file nor SSL_ca_path is set, then SSL_ca_file is implied to be the one provided by Mozilla::CA. If the Mozilla::CA module isn't available SSL requests will fail. Either install this module, set up an alternative SSL_ca_file or disable hostname verification.
This module used to be bundled with the libwww-perl, but it was unbundled in v6.02 in order to be able to declare its dependencies properly for the CPAN tool-chain. Applications that need https support can just declare their dependency on LWP::Protocol::https and will no longer need to know what underlying modules to install.