Try this:

class My_Widget extends WP_Widget {

    /**
     * Sets up the widgets name etc
     */
    public function __construct() {
        $widget_ops = array(
            'classname' => 'my_widget',
            'description' => 'My Widget is awesome',
        );
        parent::__construct('my_widget', 'My Widget', $widget_ops);
    }

    /**
     * Outputs the content of the widget
     *
     * @param array $args
     * @param array $instance
     */
    public function widget($args, $instance) {
        echo $args['before_widget'];
        echo $instance['title'];
        echo $args['after_widget'];
    }

    /**
     * Outputs the options form on admin
     *
     * @param array $instance The widget options
     */
    public function form($instance) {

        $title = !empty($instance['title']) ? $instance['title'] : esc_html__('New title', 'text_domain');
        if(isset($instance['error'])){
            echo $instance['error'];
        }
        ?>
            <p>
            <label for="<?php echo esc_attr($this->get_field_id('title')); ?>"><?php esc_attr_e('Title:', 'text_domain'); ?></label> 
            <input class="widefat" id="<?php echo esc_attr($this->get_field_id('title')); ?>" name="<?php echo esc_attr($this->get_field_name('title')); ?>" type="text" value="<?php echo esc_attr($title); ?>">
            </p>
        <?php
    }

    /**
     * Processing widget options on save
     *
     * @param array $new_instance The new options
     * @param array $old_instance The previous options
     */
    public function update($new_instance, $old_instance) {

        // !!!!!!!
        if (empty($new_instance['title'])) {
            $instance['error'] = "ERROR!! title empty";
        }else{
            $instance['title'] = strip_tags( $new_instance['title'] );
        }
        return $instance;
    }

}

you can also check for the error value in the widget function to say that the data is not valid and the widget data needs to be updated.