The above are great solutions, but there is one more.
You may have seen modules that have something like $Foo::errstr or the likes. Setting up something like that isn't too hard:

package Foo::Bar;
our $error = "";

sub new {
    my( $class, @args ) = @_;
    my $self = bless( \@args, $class );
    unless( $self->method_that_might_fail() ) {
        $Foo::Bar::error = "O noes";
        return undef;
    }
    return $self;
}
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Of course, you will have to change that to fit your style, and it is probably a good idea to push the error setting to a separate subroutine.