Thanks :-) With your help I was able to find the missing piece. Here is the working code:

my(@popup_opts) = (-popover => undef, qw/-overanchor sw -popanchor nw/
+);
my $dialogWindow = $mw->Dialog(
        @popup_opts,
        -title => "Error", -text => "My Error Message", -bitmap=>'erro
+r', -buttons => ['Ok']);
[download]

This is supposedly documented under Tk::Popup, according to http://search.cpan.org/dist/Tk/pod/DialogBox.pod, but I can't seem to find Tk::Popup documentation.