check_admin_referer
is a pluggable function which means it is defined after plugins are loaded so call your constructor or instantiate the object after or using plugins_loaded
action hook.
ex:
class MyClass{
function __construct(){
if( isset($_POST['my_nonce_field']) && check_admin_referer('my_nonce_action', 'my_nonce_field'))
$this->update_item();
}
}
add_action('plugins_loaded','newobj');
function newobj(){
$myclass = new MyClass;
}