I'd use File::Find. It's a core module, so it will always be anywhere you find Perl. It takes more code to write, but it's still not that bad:

sub find_text_files {
    my $dir = shift;

    my @text_files;
    my $tf_finder = sub {
        return if ! -f;
        return if ! /\.txt\z/;
        push @text_files, $File::Find::name;
    };
    find( $tf_finder, $dir );

    return @text_files;
}
[download]

(Not tested.)

It would be a little easier using File::Find::Rule, but that's not core.