Google reCaptcha V.2 implementation on one page checkout payment method flow in Magento 1.9

Question

I have been trying to add google recaptcha on magento checkout page where payment methods are toggled, I'm trying to invoke google re-captcha when a button is clicked but it goes through without captcha as required field before continuing, any help would be appreciated?

HTML

<button type="button" class="button" onclick="payment.save()"><span><span><?php echo $this->__('Continue') ?></span></span></button>

Google Recaptcha Code

 <script src='https://www.google.com/recaptcha/api.js'></script>
        <?php if ($this->helper('recaptcha')->showOnOnepage() == 1) { ?>
             <li id="rcode">
                 <div class="captcha">
                      <div class="g-recaptcha" data-sitekey="<?php echo $this->helper('recaptcha')->getKey(); ?>"
                           data-theme="<?php echo($this->helper('recaptcha')->getTheme()); ?>"></div>
                      </div>
                 <span id="captcha-required" style='display:none; color:#ff0000'><?php echo $this->__('Please Fill Recaptcha To Continue'); ?></span>
             </li>
        <?php } ?>

Onclick function

<script type="text/javascript">
        jQuery('.btn').click(function () {
            var payment = new Payment('co-payment-form', '<?php echo $this->getUrl('checkout/onepage/savePayment') ?>');
        <?php
            if($this->helper('recaptcha')->showOnOnepage() == 0){ ?>
            payment.save();
            <?php } else { ?>
            if (grecaptcha.getResponse() != "") {
                payment.save();
            }
            else {
                document.getElementById("captcha-required").style.display = "block";
            }
        <?php } ?>
        });
    </script>